Letteratura scientifica selezionata sul tema "Variétés irréductibles holomorphes symplectiques"
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Articoli di riviste sul tema "Variétés irréductibles holomorphes symplectiques":
Druel, Stéphane. "Invariants de Hasse-Witt des réeductions de certaines variétés symplectiques irréductibles". Michigan Mathematical Journal 61, n. 3 (settembre 2012): 615–30. http://dx.doi.org/10.1307/mmj/1347040262.
Tesi sul tema "Variétés irréductibles holomorphes symplectiques":
Denisi, Francesco Antonio. "Positivité sur les variétés irréductibles holomorphes symplectiques". Electronic Thesis or Diss., Université de Lorraine, 2023. http://www.theses.fr/2023LORR0162.
In this thesis, we study some aspects of the positivity of divisors on irreducible holomorphic symplectic (IHS) manifolds. Fix a projective IHS manifold X of complex dimension 2n. Inspired by the work of Bauer, Küronya, and Szemberg, we show that the big cone of X has a locally finite decomposition into locally rational polyhedral subcones, called Boucksom-Zariski chambers. These subcones have a geometric meaning: on any of them, the volume function is expressed by a homogeneous polynomial of degree 2n. Furthermore, in the interior of any Boucksom-Zariski chamber, the divisorial part of the augmented base locus of big divisors stays the same. After analyzing the big cone, we determine the structure of the pseudo-effective cone of X, generalizing a well-known result due to Kovács for K3 surfaces. In particular, we show that if the Picard number of X is at least 3, the pseudo-effective cone either is circular or does not contain circular parts and is equal to the closure of the cone generated by the prime exceptional divisor classes. From this result in convex geometry, we deduce some geometric properties of X and show the existence of rigid uniruled divisors on some singular symplectic varieties. We study the behaviour of the asymptotic base loci of big divisors on X, and we provide a numerical characterization for them. As a consequence of this numerical characterization, we obtain a description for the dual of the cones mathrm{Amp}_k(X), for any 1leq k leq 2n, where mathrm{Amp}_k(X) is the convex cone of big divisor classes having the augmented base locus of dimension strictly smaller than k. Using the divisorial Zariski decomposition, the Beauville-Bogomolov-Fujiki (BBF) form, and the decomposition of the big cone of X into Boucksom-Zariski chambers, we associate to any big divisor class alpha and a prime divisor E on X a polygon Delta_E(alpha) whose geometry is related to the variation of the divisorial Zariski decomposition of alpha in the big cone. Its euclidean volume is expressed in terms of the BBF form and is independent of the choice of E. We show that these polygons fit in a convex cone Delta_E(X) as slices, globalizing in this way the construction. To conclude, we show that under some hypothesis, the polygons Delta_E(alpha) can be expressed as a Minkowski sum of some polygons {Delta_E(Beta_i)}_{i in I}, for some big classes {Beta_i}_{_ iin I}. Remarkably, these polygons behave like the Newton-Okounkov bodies of big divisors on smooth projective surfaces
Bertini, Valeria. "Rational curves on irreducible symplectic varieties of OG10 type". Thesis, Strasbourg, 2019. https://publication-theses.unistra.fr/public/theses_doctorat/2019/Bertini_Valeria_2019_ED269.pdf.
Irreducible holomorphic symplectic varieties (IHSV) are the algebraic analogue of the hyperkähler Riemannian manifolds. An IHSV of dimension 2 is a K3 surface; in this case, if furthermore X is projective, any ample curve on X is linearly equivalent to a sum of rational curves (Bogomolov, Mumford). Charles, Mongardi and Pacienza proved the existence of uniruled divisors on (almost) any ample linear system on a IHSV that is deformation equivalent to an Hilbert scheme on a K3 surface, or to a generalized Kummer variety. The existence of many rational curves on X semplifies the structure of the 0-Chow group of X. In my thesis, I worked on the OG10 case, the IHSV defined by O’Grady; the variety OG10 isimportant and very actively studied. The main result of my thesis proves the existence of ample uniruled divisors on any IHSV inside three connected components of the moduli space of OG10 varieties
Deltour, Guillaume. "Propriétés symplectiques et hamiltoniennes des orbites coadjointes holomorphes". Phd thesis, Université Montpellier II - Sciences et Techniques du Languedoc, 2010. http://tel.archives-ouvertes.fr/tel-00552150.
Lazzarini, Laurent. "Courbes pseudo-holomorphes et transversalité : la conjecture d'Arnold pour les sous-variétés lagrangiennes fortement négatives". Nancy 1, 1999. http://www.theses.fr/1999NAN10202.
The main object of this work is to examine how in an almost complex manifold of any dimension a pseudo-holomorphie curve can be factorized through a somewhere injective curve, in order to get some smooth moduli space of curves. One first deals with the easy case of the closed curves, then with curves with boundary in a totally real submanifold. Contrary to a closed curve, a curve with boundary may be neither somewhere injective nor multi-covered. However it is possible to extract from its image another curve somewhere injective but still with boundary in the totally real submanifold. Moreover, if the initial curve is a disc, then the extracted disc can be 50 as weIl. As an application, one proves a special case of the Arnold conjecture for the intersection of a Lagrangian submanifold and its Hamiltonian isotopies in a symplectie manifold
Camere, Chiara. "Stabilité des images inverses des fibrés tangents et involutions des variétés symplectiques". Phd thesis, Université de Nice Sophia-Antipolis, 2010. http://tel.archives-ouvertes.fr/tel-00552994.
Perego, Arvid. "Un théorème de Gabriel pour les faisceaux cohérents tordus et groupe de Picard et 2-factorialité des exemples de O'Grady de variétés irréductibles symplectiques". Nantes, 2008. http://www.theses.fr/2008NANT2057.
This PhD thesis is divided in two parts : in the firs one, we present a generalization of Gabriel's Theorem on coherent sheaves to twisted coherent sheaves : more precisely, we show that any Noetherian scheme X can be reconstructed from its abelian category Coh(X; α) of coherent sheaves twisted by an element α in the cohomological Brauer group de X. In the second part we study the two moduli spaces M10 and M6 introduced by O'Grady, which he uses to obtain his two new examples of irreducible symplectic varieties in dimension 10 and 6. We calculate the Picard group of M10 and M6, and we show that these two varieties are not locally factorial, but 2-factorial. This is done using the results obtained by Rapagnetta on the cohomology and the Beauville-Bogomolov form of M10 and M6, and studying the properties of the Le Potier's morphism in these two cases
Perego, Arvid. "Un théorème de Gabriel pour les faisceaux cohérents tordues et Groupe de Picard et 2-factorialité des exemples de O'Grady de variétés irréductibles symplectiques". Phd thesis, Université de Nantes, 2008. http://tel.archives-ouvertes.fr/tel-00340585.
Tari, Kévin. "Automorphismes des variétés de Kummer généralisées". Thesis, Poitiers, 2015. http://www.theses.fr/2015POIT2301/document.
Ln this work, we classify non-symplectic automorphisms of varieties deformation equivalent to 4-dimensional generalized Kummer varieties, having a prime order action on the Beauville-Bogomolov lattice. Firstly, we give the fixed loci of natural automorphisms of this kind. Thereafter, we develop tools on lattices, in order to apply them to our varieties. A lattice-theoritic study of 2-dimensional complex tori allows a better understanding of natural automorphisms of Kummer-type varieties. Finaly, we classify all the automorphisms described above on thos varieties. As an application of our results on lattices, we complete also the classification of prime order automorphisms on varieties deformation-equivalent to Hilbert schemes of 2 points on K3 surfaces, solving the case of order 5 which was still open
Cattaneo, Alberto. "Non-symplectic automorphisms of irreducible holomorphic symplectic manifolds". Thesis, Poitiers, 2018. http://www.theses.fr/2018POIT2322/document.
We study automorphisms of irreducible holomorphic symplectic manifolds of type K3^[n], i.e. manifolds which are deformation equivalent to the Hilbert scheme of n points on a K3 surface, for some n > 1. In the first part of the thesis we describe the automorphism group of the Hilbert scheme of n points on a generic projective K3 surface, i.e. a K3 surface whose Picard lattice is generated by a single ample line bundle. We show that, if it is not trivial, the automorphism group is generated by a non-symplectic involution, whose existence depends on some arithmetic conditions involving the number of points n and the polarization of the surface. We also determine necessary and sufficient conditions on the Picard lattice of the Hilbert scheme for the existence of the involution.In the second part of the thesis we study non-symplectic automorphisms of prime order on manifolds of type K3^[n]. We investigate the properties of the invariant lattice and its orthogonal complement inside the second cohomology lattice of the manifold, providing a classification of their isometry classes. We then approach the problem of constructing examples (or at least proving the existence) of manifolds of type K3^[n] with a non-symplectic automorphism inducing on cohomology each specific action in our classification. In the case of involutions, and of automorphisms of odd prime order for n=3,4, we are able to realize all possible cases. In order to do so, we present a new non-symplectic automorphism of order three on a ten-dimensional family of Lehn-Lehn-Sorger-van Straten eightfolds of type K3^[4]. Finally, for n < 6 we describe deformation families of large dimension of manifolds of type K3^[n] equipped with a non-symplectic involution
Libri sul tema "Variétés irréductibles holomorphes symplectiques":
Ma, Xiaonan, e George Marinescu. Holomorphic Morse Inequalities and Bergman Kernels. Springer London, Limited, 2007.
Ma, Xiaonan, e George Marinescu. Holomorphic Morse Inequalities and Bergman Kernels (Progress in Mathematics). Birkhäuser Basel, 2007.
Capitoli di libri sul tema "Variétés irréductibles holomorphes symplectiques":
Voisin, C. "Sur la stabilité des sous-variétés lagrangiennes des variétés symplectiques holomorphes". In Complex Projective Geometry, 294–303. Cambridge University Press, 1992. http://dx.doi.org/10.1017/cbo9780511662652.022.