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Academic literature on the topic 'Complex foliations'

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Published: 7 July 2024
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Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Journal articles on the topic "Complex foliations":

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Deroin, Bertrand, and Adolfo Guillot. "Foliated affine and projective structures." Compositio Mathematica 159, no. 6 (May 15, 2023): 1153–87. http://dx.doi.org/10.1112/s0010437x2300711x.

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We formalize the concepts of holomorphic affine and projective structures along the leaves of holomorphic foliations by curves on complex manifolds. We show that many foliations admit such structures, we provide local normal forms for them at singular points of the foliation, and we prove some index formulae in the case where the ambient manifold is compact. As a consequence of these, we establish that a regular foliation of general type on a compact algebraic manifold of even dimension does not admit a foliated projective structure. Finally, we classify foliated affine and projective structures along regular foliations on compact complex surfaces.
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Mol, Rogério S. "Flags of holomorphic foliations." Anais da Academia Brasileira de Ciências 83, no. 3 (July 29, 2011): 775–86. http://dx.doi.org/10.1590/s0001-37652011005000025.

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A flag of holomorphic foliations on a complex manifold M is an object consisting of a finite number of singular holomorphic foliations on M of growing dimensions such that the tangent sheaf of a fixed foliation is a subsheaf of the tangent sheaf of any of the foliations of higher dimension. We study some basic properties oft hese objects and, in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" />, n > 3, we establish some necessary conditions for a foliation, we find bounds of lower dimension to leave invariant foliations of codimension one. Finally, still in <img src="/img/revistas/aabc/2011nahead/aop2411pcn.jpg" align="absmiddle" /> involving the degrees of polar classes of foliations in a flag.
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AZEVEDO SCÁRDUA, B. C., and J. C. CANILLE MARTINS. "ON THE GROWTH OF HOLOMORPHIC PROJECTIVE FOLIATIONS." International Journal of Mathematics 13, no. 07 (September 2002): 695–726. http://dx.doi.org/10.1142/s0129167x02001502.

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In the theory of real (non-singular) foliations, the study of the growth of the leaves has proved to be useful in the comprehension of the global dynamics as the existence of compact leaves and exceptional minimal sets. In this paper we are interested in the complex version of some of these basic results. A natural question is the following: What can be said of a codimension one (possibly singular) holomorphic foliation on a compact hermitian manifold M exhibiting subexponential growth for the leaves? One of the first examples comes when we consider the Fubini–Study metric on [Formula: see text] and dimension one foliations. In this case, under some non-degeneracy hypothesis on the singularities, we may classify the foliation as a linear logarithmic foliation. In particular, the limit set of ℱ is a union of singularities and invariant algebraic curves. Applications of this and other results we prove are given to the general problem of uniformization of the leaves of projective foliations.
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Martelo, Mitchael, and Bruno Scárdua. "On groups of formal diffeomorphisms of several complex variables." Anais da Academia Brasileira de Ciências 84, no. 4 (December 2012): 873–80. http://dx.doi.org/10.1590/s0001-37652012000400002.

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In this note we announce some results in the study of groups of formal or germs of analytic diffeomorphisms in several complex variables. Such groups are related to the study of the transverse structure and dynamics of Holomorphic foliations, via the holonomy group notion of a foliation's leaf. For dimension one, there is a well-established dictionary relating analytic/formal classification of the group, with its algebraic properties (finiteness, commutativity, solvability, among others). Such system of equivalences also characterizes the existence of suitable integrating factors, i.e., invariant vector fields and one-forms associated to the group. Our aim is to state the basic lines of such dictionary for the case of several complex variables groups. Our results are applicable in the construction of suitable integrating factors for holomorphic foliations with singularities. We believe they are a starting point in the study of the connection between Liouvillian integration and transverse structures of holomorphic foliations with singularities in the case of arbitrary codimension. The results in this note are derived from the PhD thesis "Grupos de germes de difeomorfismos complexos em várias variáveis e formas diferenciais" of the first named author (Martelo 2010).
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Scardua, Bruno Cesar Azevedo, and Liliana Jurado. "On transversely holomorphic foliations with homogeneous transverse structure." Proceedings of the International Geometry Center 16, no. 3 (November 12, 2023): 192–216. http://dx.doi.org/10.15673/pigc.v16i3.2304.

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In this paper we study transversely holomorphic foliations of complex codimension one with a transversely homogeneous complex transverse structure. We prove that the only cases are the transversely additive, affine and projective cases. We shall focus on the transversely affine case and describe the holonomy of a leaf which is "at the infinity" with respect to this structure and prove this is a solvable group. Using this we are able to prove linearization results for the foliation under the assumption of existence of some hyperbolic map in the holonomy group. Such foliations will then be given by simple-poles closed transversely meromorphic one-forms.
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Tomassini, Giuseppe. "Foliations with complex leaves." Banach Center Publications 31, no. 1 (1995): 367–72. http://dx.doi.org/10.4064/-31-1-367-372.

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Araujo, Carolina, and Paulo João Figueredo. "Foliations on Complex Manifolds." Notices of the American Mathematical Society 69, no. 07 (August 1, 2022): 1. http://dx.doi.org/10.1090/noti2507.

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Ida, Cristian. "On complex Riemannian foliations." Journal of Physics: Conference Series 670 (January 25, 2016): 012025. http://dx.doi.org/10.1088/1742-6596/670/1/012025.

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Gigante, Giuliana, and Giuseppe Tomassini. "Foliations with complex leaves." Differential Geometry and its Applications 5, no. 1 (March 1995): 33–49. http://dx.doi.org/10.1016/0926-2245(95)00004-n.

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González-Dávila, José Carmelo. "Harmonicity and minimality of complex and quaternionic radial foliations." Forum Mathematicum 30, no. 3 (May 1, 2018): 785–98. http://dx.doi.org/10.1515/forum-2017-0076.

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AbstractWe construct special classes of totally geodesic almost regular foliations, namely, complex radial foliations in Hermitian manifolds and quaternionic radial foliations in quaternionic Kähler manifolds, and we give criteria for their harmonicity and minimality. Then examples of these foliations on complex and quaternionic space forms, which are harmonic and minimal, are presented.
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Journal articles

Dissertations / Theses on the topic "Complex foliations":

1

Gutierrez, Guillen Gabriela. "Qualitative study of physical phenomena through geometry of complex foliations." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2024. http://www.theses.fr/2024UBFCK012.

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Cette thèse aborde deux sujets en physique mathématique : l'effet de la raquette de tennis et la monodromie hamiltonienne.Grâce à une exploration approfondie de la géométrie sous-jacente, nous fournissons une description mathématique complète de l'effet de la raquette de tennis, un phénomène géométrique observé dans les rotations libres de corps rigides. Nous examinons l'existence, l'origine et la robustesse de cet effet en utilisant la géométrie complexe et la géométrie réelle. Nous détectons également des signatures de contraintes physiques sur les moments d'inertie du corps, dans la structure géométrique de l'effet de la raquette de tennis. L'analyse est étendue à des phénomènes étroitement liés tels que l'effet Dhzanibekov, le monster flip et la phase de Montgomery.La deuxième partie de la thèse se concentre sur la monodromie Hamiltonienne, qui est l'obstruction topologique la plus simple à l'existence de coordonnées d'action-angles globales pour un système complètement intégrable. Nous montrons que l'utilisation de paires de Lax spectrales fournit une structure géométrique complexe qui permet l'étude de la monodromie Hamiltonienne et le calcul de la matrice de monodromie correspondante.Tout au long de ce travail de recherche, nous adoptons un cadre général qui utilise des feuilletages complexes pour fournir une structure géométrique aux problèmes posés, ce qui permet de mieux comprendre les phénomènes physiques correspondant
Through an in-depth exploration of the underlying geometry, we provide a full mathematical description of the tennis racket effect, which is a geometric phenomenon observed in free rotational dynamics of rigid bodies. We examine the existence, origin, and robustness of this effect using the interplay between complex and real geometries. We also detect signatures of physical constraints on the moments of inertia of the body, in the geometric structure of the tennis racket effect. The analysis is extended to closely related phenomena such as the Dhzanibekov effect, the monster flip, and the Montgomery phase.The second part of the thesis focuses on Hamiltonian monodromy, which is the simplest topological obstruction to the existence of global action-angle coordinates for a completely integrable system. We show that the use of spectral Lax pairs provides a complex geometric structure that enables the study of Hamiltonian monodromy and the calculation of the corresponding monodromy matrix.Throughout this research work, we adopt a general framework that employs complex foliations to provide a geometric structure for the problems under study, leading to a deeper understanding of these phenomena
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PERRONE, CARLO. "Extendable cohomologies for complex analytic varieties." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2008. http://hdl.handle.net/2108/445.

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In questa tesi introduciamo una coomologia per varietà analitiche complesse singolari (astratte). Tale coomologia, detta coomologia estendibile, viene definita a partire da opportune forme differenziali (forme differenziali estendibili) definite sulla varietà. Oltre allo studio delle proprietà generali della coomologia estendibile, mostriamo che, dato comunque un fibrato vettoriale complesso definito su una varietà, è possibile rappresentare le sue classi di Chern topologiche per mezzo delle classi di Chern estendibili (da noi definite utilizzando una teoria di tipo Chern-Weil) tramite un morfismo di integrazione da noi definito. Proviamo inoltre che le localizzazioni delle classi di Chern estendibili rapresentano le localizzazioni delle rispettive classi di Chern topologiche. Questo ci permette di ottenere un teorema dei residui astratto per varietà (analitiche complesse singolari) compatte. Come ulteriore applicazione della nostra teoria, dimostriamo un teorema dell'indice di tipo Camacho-Sad per foliazioni di varietà complesse singolari.
We introduce a cohomology, called extendable cohomology, for abstract complex singular varieties based on suitable differential forms. Aside a study of the general properties of such cohomology, we show that, given a complex vector bundle, one can compute its topological Chern classes using the extendable Chern classes, defined via a Chern-Weil type theory. We also prove that the localizations of the extendable Chern classes represent the localizations of the respective topological Chern classes, thus obtaining an abstract residue theorem for compact singular complex analytic varieties. As an application of our theory, we prove a Camacho-Sad type index theorem for holomorphic foliations of singular complex varieties.
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Belotto, Da Silva André Ricardo. "Resolution of singularities in foliated spaces." Phd thesis, Université de Haute Alsace - Mulhouse, 2013. http://tel.archives-ouvertes.fr/tel-00909798.

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Let M be an analytic manifold over the real or complex field, J be a coherent and everywhere non-zero ideal sheaf over M, E be a reduced SNC divisor and Θ an involutive singular distribution everywhere tangent to E. The main objective of this work is to obtain a resolution of singularities for the ideal sheaf J that preserves some ''good" properties of the singular distribution Θ. More precisely, the R-monomial property : the existence of local monomial first integrals. This problem arises naturally when we study the ''interaction" between a variety and a foliation and, thus, is also related with the problem of monomialization of maps and of ''quasi-smooth" resolution of families of ideal sheaves.- The first result is a global resolution if the ideal sheaf J is invariant by the singular distribution Θ;- The second result is a global resolution if the the singular distribution Θ has leaf dimension 1;- The third result is a local uniformization if the the singular distribution Θ has leaf dimension 2;We also present two applications of the previous results. The first application concerns the resolution of singularities in families, either of ideal sheaves or vector fields. For the second application, we apply the results to a dynamical system problem motivated by a question of Mattei.
4

Canales, Gonzalez Carolina. "Hypersurfaces Levi-plates et leur complément dans les surfaces complexes." Thesis, Université Paris-Saclay (ComUE), 2015. http://www.theses.fr/2015SACLS249/document.

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Dans ce mémoire nous étudions les hypersurfaces Levi-plates analytiques dans les surfaces algébriques complexes. Il s'agit des hypersurfaces réelles qui admettent un feuilletage par des courbes holomorphes, appelé le feuilletage de Cauchy Riemann (CR). Dans un premier temps nous montrons que si ce dernier admet une dynamique chaotique (i.e. s'il n'admet pas de mesure transverse invariante) alors les composantes connexes de l'extérieur de l'hypersurface sont des modifications de domaines de Stein. Ceci permet d'étendre le feuilletage CR en un feuilletage algébrique singulier sur la surface complexe ambiante. Nous appliquons ce résultat pour montrer, par l'absurde, qu'une hypersurface Levi-plate analytique qui admet une structure affine transverse dans une surface algébrique complexe possède une mesure transverse invariante. Ceci nous amène à conjecturer que les hypersurfaces Levi-plates dans les surfaces algébriques complexes qui sont difféomorphes à un fibré hyperbolique en tores sur le cercle sont des fibrations par courbes algébriques
In this work we study analytic Levi-flat hypersurfaces in complex algebraic surfaces. These are real hypersurfaces that admit a foliation by holomorphic curves, called Cauchy Riemann foliation (CR). First, we show that if this foliation admits chaotic dynamics (i.e. if it doesn't admit an invariant transverse measure), then the connected components of the complement of the hypersurface are Stein. This allows us to extend the CR foliation to a singular algebraic foliation on the ambient complex surface. We apply this result to prove, by contradiction, that analytic Levi-flat hypersurfaces admitting a transverse affine structure in a complex algebraic surface have a transverse invariant measure. This leads us to conjecture that Levi-flat hypersurfaces in complex algebraic surfaces that are diffeomorphic to a hyperbolic tori bundle over the circle are fibrations by algebraic curves
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Reis, Vinícius Soares dos. "Hipersuperfícies invariantes em dinâmica complexa." Universidade Federal de Viçosa, 2012. http://locus.ufv.br/handle/123456789/4914.

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We talk about versions the theorem of integrability Darboux - Jouanolou for endomorphisms, fields, or r-polynomial differential forms. These versions say essentially that there are infinitely many algebraic hypersurfaces invariant if and only if the dynamical system in question preserves a pencil of hypersurfaces.
Dissertamos sobre versões do teorema de integrabilidade de Darboux - Jouanolou para endomorfismos, campos ou r-formas diferenciais polinomiais. Tais versões dizem essencialmente que existem infinitas hipersuperfícies algébricas invariantes se, e somente se, o sistema dinâmico em questão preserva um pencil de hipersuperfícies.
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Trivedi, Saurabh. "Sur les stratifications réelles et analytiques complexes (a) - régulières de Whitney et Thom." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4719.

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En 1979, Trotman a démontré que les stratifications réelles lisses qui satisfont la condition de (a)-régularité sont précisément celles pour lesquelles la transversalité aux strates des applications est une condition stable dans la topologie forte. C'était un résultat surprenant puisque la (t)-régularité semblait être plus appropriée pour la stabilité de la transversalité, une erreur qui a été faite dans plusieurs articles avant que ce résultat soit montré par Trotman. Notre premier résultat est un analogue au résultat de Trotman pour la topologie faible.Il y a une dizaine d'années Trotman a demandé si le même résultat est valable pour les stratifications analytiques complexes. Dans ce travail on démontre un analogue du résultat de Trotman dans le cas complexe, en utilisant la notion de variété de Oka introduite par Forstneric et on montre que la conjecture n'est pas vraie en général en donnant des contre-exemples.Dans sa thèse, Trotman a formulé une conjecture pour généraliser son résultat pour les stratifications (a_f)-régulières de Thom. Dans une tentative de résolution de cette conjecture on a observé que la transversalité par rapport à un feuilletage est une condition stable, cependant ce n'est pas une condition générique. Donc, en voulant imiter la preuve de Trotman on ne pourra pas obtenir cette généralisation. Néanmoins, on donne ici une preuve de cette conjecture. Ce résultat peut être résumé en disant que les (a_f)-défauts dans une stratification peuvent être détectés en perturbant les applications transverses au feuilletage induit par f. Certaines techniques pour détecter (a_f)-défauts sont aussi données vers la fin
Trotman in 1979 proved that real smooth stratifications which satisfy the condition of $(a)$-regularity are precisely those stratifications for which transversality to the strata of smooth mappings is a stable condition in the strong topology. This was a surprising result since $(t)$-regularity seemed to be more appropriate for stability of transversality, a mistake that was made in several articles before this result of Trotman. Our first result is an analogue of this result of Trotman for the weak topology.Trotman asked more than ten years ago whether a similar result holds for complex analytic stratifications. We will give an analogue of Trotman's result in the complex setting using Forstneriv c's notion of Oka manifolds and show that the result is not true in general by giving counterexamples.In his Ph.D. thesis Trotman conjectured a generalization of his result for Thom $(a_f)$-regular stratifications. In an attempt to prove this conjecture we noticed that while transversality to a foliation is a stable condition, it is not generic in general. Thus, mimicking the proof of the result of Trotman would not suffice to obtain this generalization. Nevertheless, we will present a proof of this conjecture in this work. This result can be summarized by saying that Thom $(a_f)$-faults in a stratification can be detected by perturbation of maps transverse to the foliation induced by $f$. Some other techniques of detecting $(a_f)$-faults are also given towards the end
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Ben, Charrada Rochdi. "Cohomologie de Dolbeault feuilletée de certaines laminations complexes." Phd thesis, Université de Valenciennes et du Hainaut-Cambresis, 2013. http://tel.archives-ouvertes.fr/tel-00871710.

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Dans cette thèse, nous nous s'intéressons au calcul des groupes de cohomologie de Dolbeault feuilletée H0∗L (M) de certaines laminations complexes. Ceci revient à résoudre le problème du ∂ le long des feuilles ∂Lα = ω. (Ici M est un espace métrique ou une variété dans le cas où L est un feuilletage F.) Trois situations ont été étudiées de manière explicite.1. Soit M = Ω un ouvert de C × R muni du feuilletage F dont les feuilles sont les sections Ωt = {z ∈ C : (z, t) ∈ Ω} ; on dira que F est le feuilletage canonique de Ω. Sous certaines conditions sur Ω et de croissance sur la forme feuilletée ω, nous montrons que l''équation ∂Fα = ω a une solution.2. On se donne une suite (αn)n≥1 strictement croissante avec α1 = −1 et convergeant vers 1. Dans C × R on considère les points A = (0, 1) et An = (0, αn) pour n ≥ 1. Pour tout n ≥ 1, soient Sn la sphère de C × R de diamètre le segment [AnA] et E la réunion de toutes ces sphères. Alors E est un sous-espace métrique compact et connexe de C × R. Soit γ : E −→ E l'homéomorphisme défini par γ(w,u) = (ρn(w),u) lorsque (w, u) ∈ Sn où ρn est la rotation dans C d'angle 2πn. La suspension de γ donne une lamination complexe L dont les feuilles sont des surfaces de Riemann toutes équivalentes à C*. Pour cet exemple, nous montrons que l'espace vectoriel H01(L) est nul.3. On considère la variété M = C × Rn \ {(0, 0)} (les coordonnées d'un point seront notées (z,t)) qu'on munit du feuilletage complexe F défini par le système différentiel dt1 = * * * = dn = 0. Le difféomorphisme γ : (z, t) ∈ Mf7−→ (λz, λt) ∈ M (avec 0 < λ < 1) agit sur M de façon libre et propre ; en plus, c'est un automorphisme de F ; F induit alors sur le quotient M = M/γ (qui est difféomorphe 'à Sn+1 × S1) un feuilletage complexe F par surfaces de Riemann. Nous montrons que les espaces vectoriels de cohomologie de Dolbeault feuilletée H00 F (M) et H01F (M) sont isomorphes à C.
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Chen, Zhangchi. "Differential invariants of parabolic surfaces and of CR hypersurfaces; Directed harmonic currents near non-hyperbolic linearized singularities; Hartogs’ type extension of holomorphic line bundles; (Non-)invertible circulant matrices On differential invariants of parabolic surfaces A counterexample to Hartogs’ type extension of holomorphic line bundles Directed harmonic currents near non-hyperbolic linearized singularities Affine Homogeneous Surfaces with Hessian rank 2 and Algebras of Differential Invariants On nonsingularity of circulant matrices." Thesis, université Paris-Saclay, 2021. http://www.theses.fr/2021UPASM005.

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La thèse se compose de 6 articles. (1) Nous calculons les générateurs des SA₃(ℝ)-invariants pour les surfaces paraboliques. (2) Nous calculons les invariants rigides relatifs pour les hypersurfaces rigides 2-non-dégénérées de rang de Levi constant 1 dans ℂ³: V₀, I₀, Q₀ ayant 11, 52, 824 monômes au numérateur. (3) Nous organisons tous les modèles affinement homogènes non-dégénérés dans ℂ³ en branches inéquivalentes. (4) Pour un courant harmonique dirigé autour d'une singularité linéarisée non-hyperbolique qui ne charge pas les séparatrices triviales dont l'extension triviale à travers 0 est ddc-fermée, nous démontrons que le nombre de Lelong en 0 est : 4.1) strictement positif si λ>0 ; 4.2) nul si λ est rationnel et négatif ; 4.3) nul si λ est négatif et si T est invariant sous l'action d'un sous-groupe cofini du groupe de monodromie. (5) Nous construisons des fibrés holomorphes en droites en toute dimension n>=2 non-prolongeables au sens de Hartogs. (6) Nous montrons que les matrices circulantes ayant k entrées 1 et k+1 entrées 0 dans leur première rangée sont toujours non singulières lorsque 2k+1 est soit une puissance d'un nombre premier, soit un produit de deux nombres premiers distincts. Pour tout autre entier 2k+1, nous exhibons une matrice circulante singulière
The thesis consists of 6 papers. (1) We calculate the generators of SA₃(ℝ)-invariants for parabolic surfaces. (2) We calculate rigid relative invariants for rigid constant Levi-rank 1 and 2-non-degenerate hypersurfaces in ℂ³: V₀, I₀, Q₀ having 11, 52, 824 monomials in their numerators. (3) We organize all affinely homogeneous nondegenerate surfaces in ℂ³ in inequivalent branches. (4) For a directed harmonic current near a non-hyperbolic linearized singularity which does not give mass to any of the trivial separatrices and whose trivial extension across 0 is ddc-closed, we show that the Lelong number at 0 is: 4.1) strictly positive if the eigenvalue λ>0; 4.2) zero if λ is a negative rational number; 4.3) zero if λ<0 and if T is invariant under the action of some cofinite subgroup of the monodromy group. (5) We construct non-extendable, in the sense of Hartogs, holomorphic line bundles in any dimension n>=2. (6) We show that circulant matrices having k ones and k+1 zeros in the first row are always nonsingular when 2k+1 is either a power of a prime, or a product of two distinct primes. For any other integer 2k+1 we exhibit a singular circulant matrix
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Liu, Jie. "Géométrie des variétés de Fano : sous-faisceaux du fibré tangent et diviseur fondamental." Thesis, Université Côte d'Azur (ComUE), 2018. http://www.theses.fr/2018AZUR4038/document.

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Cette thèse est consacrée à l'étude de la géométrie des variétés de Fano complexes en utilisant les propriétés des sous-faisceaux du fibré tangent et la géométrie du diviseur fondamental. Les résultats principaux compris dans ce texte sont : (i) Une généralisation de la conjecture de Hartshorne: une variété lisse projective est isomorphe à un espace projectif si et seulement si son fibré tangent contient un sous-faisceau ample.(ii) Stabilité du fibré tangent des variétés de Fano lisses de nombre de Picard un : à l'aide de théorèmes d'annulation sur les espaces hermitiens symétriques irréductibles de type compact M, nous montrons que pour presque toute intersection complète générale dans M, le fibré tangent est stable. La même méthode nous permet de donner une réponse sur la stabilité de la restriction du fibré tangent de l'intersection complète à une hypersurface générale.(iii) Non-annulation effective pour des variétés de Fano et ses applications : nous étudions la positivité de la seconde classe de Chern des variétés de Fano lisses de nombre de Picard un. Ceci nous permet de montrer un théorème de non-annulation pour les variétés de Fano lisses de dimension n et d'indice n-3. Comme application, nous étudions la géométrie anticanonique des variétés de Fano et nous calculons les constantes de Seshadri des diviseurs anticanoniques des variétés de Fano d'indice grand.(iv) Diviseurs fondamentaux des variétés de Moishezon lisses de dimension trois et de nombre de Picard un : nous montrons l'existence d'un diviseur lisse dans le système fondamental dans certain cas particulier
This thesis is devoted to the study of complex Fano varieties via the properties of subsheaves of the tangent bundle and the geometry of the fundamental divisor. The main results contained in this text are:(i) A generalization of Hartshorne's conjecture: a projective manifold is isomorphic to a projective space if and only if its tangent bundle contains an ample subsheaf.(ii) Stability of tangent bundles of Fano manifolds with Picard number one: by proving vanishing theorems on the irreducible Hermitian symmetric spaces of compact type M, we establish that the tangent bundles of almost all general complete intersections in M are stable. Moreover, the same method also gives an answer to the problem of stability of the restriction of the tangent bundle of a complete intersection on a general hypersurface.(iii) Effective non-vanishing for Fano varieties and its applications: we study the positivity of the second Chern class of Fano manifolds with Picard number one, this permits us to prove a non-vanishing result for n-dimensional Fano manifolds with index n-3. As an application, we study the anticanonical geometry of Fano varieties and calculate the Seshadri constants of anticanonical divisors of Fano manifolds with large index.(iv) Fundamental divisors of smooth Moishezon threefolds with Picard number one: we prove the existence of a smooth divisor in the fundamental linear system in some special cases
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Firsova, Tatiana. "Dynamical Foliations." Thesis, 2010. http://hdl.handle.net/1807/26148.

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This thesis is devoted to the study of foliations that come from dynamical systems. In the first part we study foliations of Stein manifolds locally given by vector fields. The leaves of such foliations are Riemann surfaces. We prove that for a generic foliation all leaves except for not more than a countable number are homeomorphic to disks, the rest are homeomorphic to cylinders. We also prove that a generic foliation is complex Kupka-Smale. In the second part of the thesis we study complex H\'non maps. The sets of points $U^+$ and $U^-$ that have unbounded forward and backwards orbits correspondingly, is naturally endowed with holomorphic foliations $^+$ and $^-$. We describe the critical locus -- the set of tangencies between these foliations -- for H\'{e}non maps that are small perturbations of quadratic polynomials with disconnected Julia set.

Books on the topic "Complex foliations":

1

1943-, Camacho César, and Instituto de Matemática Pura e Aplicada (Brazil), eds. Complex analytic methods in dynamical systems: IMPA, January 1992. Paris, France: Société mathématique de France, 1994.

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Neto, Alcides Lins, and Bruno Scárdua. Complex Algebraic Foliations. de Gruyter GmbH, Walter, 2020.

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Neto, Alcides Lins, and Bruno Scárdua. Complex Algebraic Foliations. de Gruyter GmbH, Walter, 2020.

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Neto, Alcides Lins, and Bruno Scárdua. Complex Algebraic Foliations. de Gruyter GmbH, Walter, 2020.

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Complex manifolds, foliations, and uniformization. Paris: Société Mathématique de France, 2011.

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Braid foliations in low-dimensional topology. Springer, 2017.

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Farb, Benson, and Dan Margalit. Teichmuller Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691147949.003.0012.

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This chapter focuses on the metric geometry of Teichmüller space. It first explains how one can think of Teich(Sɡ) as the space of complex structures on Sɡ. To this end, the chapter defines quasiconformal maps between surfaces and presents a solution to the resulting Teichmüller's extremal problem. It also considers the correspondence between complex structures and hyperbolic structures, along with the Teichmüller mapping, Teichmüller metric, and the proof of Teichmüller's uniqueness and existence theorems. The fundamental connection between Teichmüller's theorems, holomorphic quadratic differentials, and measured foliations is discussed as well. Finally, the chapter describes the Grötzsch's problem, whose solution is tied to the proof of Teichmüller's uniqueness theorem.

Book chapters on the topic "Complex foliations":

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Waliszewski, Włodzimierz. "Complex Premanifolds and Foliations." In Deformations of Mathematical Structures, 65–78. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2643-1_7.

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Scárdua, Bruno. "Foliations on Complex Projective Spaces." In Holomorphic Foliations with Singularities, 91–114. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76705-1_9.

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Scárdua, Bruno. "Some Results from Several Complex Variables." In Holomorphic Foliations with Singularities, 11–16. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76705-1_2.

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Ilyashenko, Yulij, and Sergei Yakovenko. "Global properties of complex polynomial foliations." In Graduate Studies in Mathematics, 469–597. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/gsm/086/05.

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Gromoll, Detlef, and Karsten Grove. "One-Dimensional Metric Foliations in Constant Curvature Spaces." In Differential Geometry and Complex Analysis, 165–68. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69828-6_11.

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Camacho, César, and Maria Izabel Camacho. "Complex Foliations Arising from Polynomial Differential Equations." In Bifurcations and Periodic Orbits of Vector Fields, 1–18. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-015-8238-4_1.

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Novikov, Dmitry, and Sergei Yakovenko. "Rolle Models in the Real and Complex World." In Handbook of Geometry and Topology of Singularities V: Foliations, 281–334. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-52481-3_6.

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Cavalier, Vincent, and Daniel Lehmann. "Bounding from below the Degree of an Algebraic One-dimensional Foliation Having a Prescribed Algebraic Solution." In Real and Complex Singularities, 47–51. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/978-3-7643-7776-2_5.

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Guillot, Adolfo. "On the Singularities of Complete Holomorphic Vector Fields in Dimension Two." In Handbook of Geometry and Topology of Singularities VI: Foliations, 1–37. Cham: Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-54172-8_1.

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Fernandez, Francisco J., and Alberto Marcos. "Mylonitic Foliation Developed by Heterogeneous Pure Shear under High-Grade Conditions in Quartzofeldspathic Rocks (Chímparra Gneiss Formation, Cabo Ortegal Complex, NW Spain)." In Proceedings of the International Conferences on Basement Tectonics, 17–34. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-009-1598-5_2.

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Conference papers on the topic "Complex foliations":

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Asuke, Taro. "ON THE JULIA SETS OF COMPLEX CODIMENSION-ONE TRANSVERSALLY HOLOMORPHIC FOLIATIONS." In Proceedings of the VIII International Colloquium. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789814261173_0006.

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Zhu, X., M. Serati, E. Mutaz, and Z. Chen. "True Triaxial Testing of Anisotropic Solids." In 56th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2022. http://dx.doi.org/10.56952/arma-2022-2125.

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ABSTRACT: Accurate determination of rock mechanical properties (particularly sedimentary shales, mica and schists with foliation and bedding planes) is critical to the safe design and excavation of underground mines and tunnels. Traditional techniques to calculate rock elastic properties often involve testing cylindrical or disc-shaped specimens under uniaxial compression or diametrical loading. But, these stress conditions may not represent the actual stress state under which rock is subjected at depth. A true triaxial testing technique on cubed specimens are, therefore, preferred as it better represents field stress conditions. This paper introduces and verifies a modified step-compression true-triaxial based technique to measure the elastic constants in fibre-reinforced epoxy samples, selected as a low-porosity anisotropic solid. The elastic constants obtained from the proposed method (even under higher stress levels) are found to be in good agreement with results from the benchmark tests with uniaxial compression but in the meanwhile offers other anisotropic parameters, which cannot be obtained from conventional measurements. 1. INTRODUCTION Accurate determination of rock directional elastic properties has always been a hot topic in rock mechanics with immediate applications in most geotechnical and mining engineering (Eberli et al., 2003). While rock is frequently treated as a CHILE (continuous, homogeneous, isotropic, and linearly elastic) medium, this assumption provides only limited insight into the true rock mass deformations (Chou & Chen, 2008; Serati, Alehossein, & Williams, 2016). A more practical rock behavior is therefore the consideration of rock anisotropy, since many rocks exposed near the Earth’s surface show various levels of directionally dependent properties due to bedding, stratification, foliation, fissuring, schistosity, jointing, and faulting (Amadei, 1996). In the stress-strain relationship study for a loaded rock sample, rock behavior can be generally classified into four categories: isotropic, transversely isotropic, orthotropic, and anisotropic. The number of elastic constants to represent the stress-strain relation of a complete anisotropic rock is 21. However, due to the elastic symmetry of three isotropic planes, the number of stiffness constants of an orthotropic material can be reduced to nine (9) constants only. It can be further reduced to five elastic parameters for a transversely isotropic material (E1, E2, ν1, ν2, and G2) and two (namely the Poisson’s ratio and Young’s modulus) for a perfectly isotropic material, where the subscripts "1" and "2" refer to in-plane and out-of-plane directions in transversely isotropic materials (Ding et al., 2006).

Reports on the topic "Complex foliations":

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Boily-Auclair, É., P. Mercier-Langevin, P. S. Ross, and D. Pitre. Alteration and ore assemblages of the LaRonde Zone 5 (LZ5) deposit and Ellison mineralized zones, Doyon-Bousquet-LaRonde mining camp, Abitibi, Quebec. Natural Resources Canada/CMSS/Information Management, 2022. http://dx.doi.org/10.4095/329637.

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The LaRonde Zone 5 (LZ5) mine is part of the Doyon-Bousquet-LaRonde mining camp and is located in the southern part of the Abitibi greenstone belt in northwestern Quebec. The LZ5 deposit consists of three stacked mineralized corridors: Zone 4, Zone 4.1, and Zone 5. Zones 4 and 4.1 are discontinuous satellite mineralized corridors, whereas Zone 5 represents the main mineralized body. The mineralized zones of the LZ5 deposit and adjacent Ellison property (Ellison A and B zones) are hosted in the strongly-deformed, 2699-2695 Ma transitional to calcalkaline, intermediate to felsic, volcanic and volcaniclastic rocks of the Bousquet Formation upper member, which is part of the Blake River Group (2704-2695 Ma). Zones 4, 4.1, and 5 at the LZ5 mine are hosted in intermediate volcanic and volcaniclastic rocks of the Westwood andesitic to rhyodacitic unit (unit 5.1a), which forms the base of the upper member of the Bousquet Formation. The Ellison Zone A is hosted higher up in the stratigraphic sequence within a newly described intermediate volcanic unit. The Ellison Zone B is hosted in felsic volcanic and volcaniclastic rocks of the Westwood feldsparphyric rhyolite dome (subunit 5.3a-(b)). Mineralization in all three zones of the LZ5 deposit consists of discordant networks of millimeter- to centimeter-thick pyrite ±chalcopyrite ±sphalerite ±pyrrhotite veins and veinlets (10-20 % of the volume of the rock) and, to a lesser extent, very finely disseminated pyrite and boudinaged veins (less than or equal to 5 vol. % each) in strongly altered host rocks. Gold commonly occurs as microscopic inclusions in granoblastic pyrite and at the triple junction between recrystallized grains. The veins, stockworks, and disseminations were intensely folded and transposed in the steeply south-dipping, east-west trending S2 foliation. The vein network is at least partly discordant to the stratigraphy. A distal alteration halo envelops the LZ5 mineralized corridors and consists of a sericite-carbonate-chlorite- feldspar ±biotite assemblage. A proximal sericite-carbonate-chlorite-pyrite-quartz- feldspar-biotite ±epidote alteration assemblage is present within the LZ5 mineralized zones. A local proximal alteration assemblage of sericite-quartz-pyrite is also locally developed within Zone 4 and Zone 5 of the LZ5 deposit. Mass gains in Fe2O3 (t) and K2O, and mass losses in CaO, MgO, Na2O, and locally SiO2, are characteristic of the LZ5 alteration zones. The Ellison zone A and B are similar to LZ5 in terms of style of mineralization, but thin (10-20 cm) veins or bands of semi-massive to massive, finely recrystallized disseminated pyrite (0.1-1 mm) are distinctive. Chalcopyrite and sphalerite are also slightly more abundant in the mineralized corridors of the Ellison property and are usually associated with elevated gold grades. The zones are also slightly richer than at LZ5 in terms of gold and silver content, but narrower and less continuous in general. The Ellison Zone A is characterized by gains in Fe2O3 (t) and K2O and losses in CaO, MgO, Na2O, and SiO2. Gains in Fe2O3 (t) and local gains in K2O, MgO, and MnO, and losses in CO2, Na2O, P2O5, and SiO2, characterize the felsic host rocks of the Zone B corridor. The style of mineralization at LZ5 (pyrite ±chalcopyrite veins and veinlets, ±disseminated pyrite with low base metal content), its setting (i.e. in rocks of intermediate composition at the base of the upper member of the Bousquet Formation), and the geometry of its ore zones (stacked lenses of sulfide veins and veinlets, without massive sulfide lenses) differ from the other major deposits of the Doyon-Bousquet-LaRonde mining camp. Despite these differences, this study indicates that the LZ5 and Ellison mineralized corridors are of synvolcanic hydrothermal origin and have most likely been formed by convective circulation of seawater below the seafloor. An influx of magmatic fluids from the Mooshla synvolcanic intrusive complex or its parent magma chamber could explain the Au enrichment at LZ5, as has been suggested for other deposits of the camp. Evidence for a pre-deformation synvolcanic mineralization at LZ5 includes ductile deformation and recrystallization of the sulfides, the stacked nature of its ore zones, subconcordant alteration halos that envelop the mineralized corridors, evidence that the mineralized system was already active when the LZ5 lenses were deposited and control on mineralization by primary volcanic features such as the permeability and porosity of the volcanic rocks.

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