Dissertations / Theses on the topic 'Positivity of line bundles'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 22 dissertations / theses for your research on the topic 'Positivity of line bundles.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
Fang, Yanbo. "Study of positively metrized line bundles over a non-Archimedean field via holomorphic convexity." Thesis, Université de Paris (2019-....), 2020. http://www.theses.fr/2020UNIP7033.
This thesis is devoted to the study of semi-positively metrized line bundles in non-Archimedean analytic geometry, with the point of view of functional analysis over an ultra-metric field exploiting the geometry related to holomorphic convexity. The first chapter gathers some preliminaries about Banach algebras over ultra-metric fields and the geometry of their spectrum in the sense of V. Berkovich, which is the framework of our study. The second chapter present the basic construction, which encodes the related geometric information into some Banach algebra. We associate the normed algebra of sections of a metrized line bundle. We describe its spectrum, relating it with the dual unit disc bundle of this line bundle with respect to the envelope metric. We thus encode the metric positivity into the holomorphic convexity of the spectrum. The third chapter consists of two independent for the normed extension problem for restricted sections on a sub-variety. We obtain an upper bound for the asymptotic norm distorsion between the restricted section and the extended one, which is uniform with respect to the choice of restricted sections. We use a particular property of affinoid algebras to obtain this inequality. The fourth chapter treat the problem of regularity of the envelope metric. With a new look from the holomorphic analysis of several variables, we aime at showing that on ample line bundles, the envelop metric is continuous once the original metric is. We suggest a tentative approach based on a speculative analogue of Cartan-Thullen’s result in the non-Archimedean setting
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
Jabbusch, Kelly. "Notions of positivity for vector bundles /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5772.
Granja, Gustavo 1971. "On quaternionic line bundles." Thesis, Massachusetts Institute of Technology, 1999. http://hdl.handle.net/1721.1/85302.
Ottem, John Christian. "Ample subschemes and partially positive line bundles." Thesis, University of Cambridge, 2013. https://www.repository.cam.ac.uk/handle/1810/265577.
Taylor, Lawrence. "Noncommutative tori, real multiplication and line bundles." Thesis, University of Nottingham, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437094.
Bedi, Harpreet Singh. "Line Bundles of Rational Degree Over Perfectoid Space." Thesis, The George Washington University, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10681242.
In this thesis we lay the foundation for rational degree d as an element of Z[1/p] by using perfectoid analogue of projective space, and consider power series instead of polynomials. We start the groundwork by proving Weierstrass theorems for perfectoid spaces which are analogues of standard Weierstrass theorems in complex analysis. We then move onto defining sheaves for Projective perfectoid analogue and prove perfectoid analogues of Gorthendieck's classication theorem on projective line, Serre's theorem on Cohomology of line bundles. As intermediate results we also compute Picard groups and describe Cartier and Weil divisors for Perfectoid.
Andrews, Patrick Rowan. "Boiling on in-line and staggered tube bundles." Thesis, Heriot-Watt University, 1985. http://hdl.handle.net/10399/1608.
Petersen, Lars [Verfasser]. "Line bundles on complexity-one T-varieties and beyond / Lars Petersen." Berlin : Freie Universität Berlin, 2011. http://d-nb.info/1025240324/34.
Herrmann, Hendrik [Verfasser], George [Gutachter] Marinescu, and Silvia [Gutachter] Sabatini. "Bergman Kernel Asymptotics for Partially Positive Line Bundles / Hendrik Herrmann ; Gutachter: George Marinescu, Silvia Sabatini." Köln : Universitäts- und Stadtbibliothek Köln, 2018. http://d-nb.info/1193177243/34.
Knöppel, Felix Jakob [Verfasser], Ulrich [Akademischer Betreuer] Pinkall, Ulrich [Gutachter] Pinkall, Boris [Gutachter] Springborn, and Johannes [Gutachter] Wallner. "Complex line bundles over simplicial complexes / Felix Jakob Knöppel ; Gutachter: Ulrich Pinkall, Boris Springborn, Johannes Wallner ; Betreuer: Ulrich Pinkall." Berlin : Technische Universität Berlin, 2016. http://d-nb.info/1156013682/34.
Wang, Huan [Verfasser], George [Gutachter] Marinescu, and Alexander [Gutachter] Lytchak. "On the Growth of Dimension of Harmonic Spaces of Semipositive Line Bundles over Manifolds / Huan Wang. Gutachter: George Marinescu ; Alexander Lytchak." Köln : Universitäts- und Stadtbibliothek Köln, 2016. http://d-nb.info/1110012365/34.
Hoff, Michael [Verfasser], and Frank-Olaf [Akademischer Betreuer] Schreyer. "Osculating cones to Brill–Noether loci for line and vector bundles on curves and relative canonical resolutions of curves / Michael Hoff ; Betreuer: Frank-Olaf Schreyer." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2017. http://d-nb.info/112873561X/34.
Wang, Jie. "Geometry of general curves via degenerations and deformations." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1291067498.
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.
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
Ancona, Michele. "Moments en géométrie algébrique réelle." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1274.
It is well known that the number of real roots of a real degree d polynomial is at most d. In the 90s, E. Kostlan proved that the average number of real roots equals the square root of d, once we equip the space of polynomials with some natural Gaussian measure. This result has a geometric interpretation, in which the real polynomials are sections of a line bundle over the Riemann sphere. We can extend this study in a more general case of a real Riemann surface equipped with ample line bundle and study the expected value of the number of real zeros of a random section. In this thesis, we compute all the central moments of these random variables. As an application, we prove that the measure of the space of real sections whose number of real zeros deviates from the expected one goes to zeros, as the degree of the line bundle goes to infinity.In a second part, we present analogues results in real Hurwitz theory, in which we study the real critical points of a random branched covering of the Riemann sphere. We compute the expected value of this number and also all the central moments.The techniques we use are of analytique nature (Bergman kernel, L^2 estimates) and gometric one (Olver multispaces, coarea formula)
Karlsson, Cecilia. "Orienting Moduli Spaces of Flow Trees for Symplectic Field Theory." Doctoral thesis, Uppsala universitet, Algebra och geometri, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-269551.
Pelletier, Maxime. "Résultats de stabilité en théorie des représentations par des méthodes géométriques." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE1228/document.
The Kronecker coefficients, which are indexed by triples of partitions and describe how the tensor product of two irreducible representations of the symmetric group decomposes as a direct sum of such representations, were introduced by Francis Murnaghan in the 1930s. He notably noticed a remarkable behaviour of these coefficients: from any triple of partitions, one can construct a particular sequence of Kronecker coefficients which eventually stabilises.In order to generalise this property, John Stembridge introduced in 2014 a notion of stability for triples of partitions, as well as another notion -- of weakly stable triple -- about which he conjectured that it should be equivalent to the previous one. This conjecture was proven shortly after by Steven Sam and Andrew Snowden, with algebraic methods.In this thesis we especially give another proof -- this time geometric -- of this equivalence, using the classical expression of the Kronecker coefficients as dimensions of spaces of sections of line bundles on flag varieties. With these methods we can also be interested in more specific questions: since the stability which we discuss means that some sequences of coefficients stabilise, one can wonder at which point these sequences become constant.We then apply these techniques to other examples of branching coefficients, and are also interested in another problem: how can we produce stable triples of partitions? We thus generalise a result obtained independently by Laurent Manivel and Ernesto Vallejo on this subject
Liu, Linyuan. "Cohomologie des fibrés en droites sur SL3/B en caractéristique positive : deux filtrations et conséquences." Thesis, Sorbonne université, 2019. http://www.theses.fr/2019SORUS229.
Let G be a semi-simple algebraic group over an algebraically closed field of positive characteristic. The cohomology of G-equivariant line bundles over G/B induced by a character of B are important objects in the representation theory of G. In this thesis, we concentrate on G = SL3. In the first chapter,we prove the existence of a two-step filtration of H1(μ) and H2(μ) when μ is in the closure of the Griffith region. In the second chapter, we prove the existence ofa p-Hi-D-filtration of Hi(μ) for all i and μ, which generalizes the p-filtration ofH0(μ) introduced by Jantzen. In the third chapter, we study and determine the structure of the modules appearing in the p-Hi-D-filtration. In the last chapter,we give an explicit and combinatorial description of H2(μ) for μ in the Griffith region and we generalize this description to Hd(G/B, μ) for G = SLd+1 and certain weights μ
Gonçalves, Alexandre Casassola. "An application of the continuity method for an equation on line bundles." Thesis, 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3099452.
Ascah-Coallier, Isabelle. "Le théorème de Borel-Weil-Bott." Thèse, 2008. http://hdl.handle.net/1866/7875.
Jauffret, Colin. "Modules réflexifs de rang 1 sur les variétés nilpotentes." Thèse, 2016. http://hdl.handle.net/1866/19543.
Let G be a simple, connected, simply connected complex linear algebraic group with parabolic subgroup P G and nilpotent ideal n p. The proper collapsing map G x P n = Gn factors through the normal affine variety N := SpecC [G x P n] which is called a nilpotent variety. Assuming the collapsing is generically finite, we describe the equivariant divisor class group of N using rank 1 reflexive equivariant C[N]-modules. A representative of each class may be chosen as global sections of a line bundle over G x P' n' where G x P' n' = Gn' is a possibly distinct collapsing that factors through the same nilpotent variety. Assuming either G is of type A or the collapsing comes from specific weighted Dynkin diagrams,we showthat each representative arise from a weight that may be chosen dominant. Moreover, if the module represents a torsion element within the class group, then it is Cohen– Macaulay and we deduce a cohomological vanishing theorem.