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Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 39 for “"Vector bundles."”.
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Rational families of vector bundles on curves
… curves on moduli spaces M of rank 2 stable vector bundles with odd determinant on curves C of genus g [greater than or equal to] 2. We prove that the maximally rationally connected quotient of such a component is either the Jacobian J(C) or a direct sum of two copies of the Jacobian. We show …
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Bergman kernel and stability of holomorphic vector bundles with sections
… notion of asymptotic stability for a holomorphic vector bundle with a global holomorphic section on a projective manifold. We prove that the special metric on the bundle studied by Bradlow is the limit of a sequence of balanced metrics that are induced from the asymptotic stability. Conversely, …
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Splitting of Vector Bundles on Punctured Spectrum of Regular Local Rings
<p>In this dissertation we study splitting of vector bundles of small rank on punctured spectrum of regular local rings. We give a splitting criterion for vector bundles of small rank in terms of vanishing of their intermediate cohomology modules <em>H<sup>i</sup>(U, E</em>)<sub>2_i_n−3</sub>, …
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Smooth Stratified Vector Bundles and Obstructions to Their Orthonormal Frame Bundles
… of a stratified space, which is no longer a vector bundle, we begin the construction of a general theory of smooth stratified vector bundles. We show that one can construct a frame bundle of a smooth stratified vector bundle in a canonical way, but that there are substantial obstructions to …
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Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
This thesis includes two parts. In the first part, we show a purity theorem for stratifications by Newton polygons coming from crystalline cohomology, which says that the family of Newton polygons over a noetherian scheme have a common break point if this is true outside a subscheme of codimension …
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Four Generated Rank 2 Arithmetically Cohen-Macaulay Vector Bundles on General Sextic Surfaces
… 2 arithmetically Cohen-Macaulay: ACM for short) bundles on a general sextic surface.</p><p>In Chapter One we introduce preliminaries and prove on a general sextic surface, every four generated indecomposable rank 2 ACM bundle belongs to one of fourteen cases. In Chapter Two we prove for each of …
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Asymptotics of the Yang-Mills Flow for Holomorphic Vector Bundles over Kahler Manifolds
… the Yang-Mills flow associated to a holomorphic vector bundle $E$ over an arbitrary K"{a}hler manifold $(X,omega )$. In particular we show that the flow is determined at infinity by the holomorphic structure of $E$. Namely, if we fix an integrable unitary reference connection $A_{0}$ defining the …
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Limit linear series in positive characteristic and Frobenius-unstable vector bundles on curves
… of a result of Mochizuki Frobenius-unstable bundles for C general, and hence obtaining a self-contained proof of the resulting formula for the degree of V₂.
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Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space
… different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this …
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The homotopy type of the matroid Grassmannian
… Since the classifying spaces for rank k matroid bundles and rank k vector bundles are, respectively, obtained by taking colimits of the above spaces as n grows, this result provides a natural equivalence between the functors of matroid bundles and vector bundles. This, in turn, has implications …
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Realising The Smooth Representations Of GL2(O_F) Using p-adic Geometric Methods
… in order to develop a theory of G-equivariant vector bundles with a flat connection on X. In the case that X is affinoid and connected, the de Rham cohomology groups of these vector bundles on X are a source of smooth representations of G. By applying this theory to GL_2(O_F)-stable (dagger) …
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Bott Periodicity
… the generalized cohomology theory defined by vector bundles. This paper examines the proof, given by Atiyah and Bott[3], of the periodicity theorem for the complex case. We also describe the long exact sequence for K-cohomology in the category of connected finite CW-complexes.
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Motivic symmetric ring spectrum representing algebraic K-theory
… and solved by introducing a category of vector bundles with strictly associative tensor product that is also strictly commutative with line bundles.
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Applications of Numerical Methods in Heterotic Calabi-Yau Compactification
… connections on poly-stable holomorphic vector bundles over those spaces. We apply the numerical techniques for obtaining Ricci-flat metrics to study hierarchies of curvature scales over Calabi-Yau manifolds as a function of their complex structure moduli. The work we present successfully …
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cdh descent for homotopy Hermitian K-Theory of rings with involution
… space of automorphism groups of Hermitian vector bundles over a ring with involution with 2 invertible; this generalizes a result of Schlichting-Tripathi. We then prove a periodicity theorem for Hermitian K-theory and use it to construct an E-infinity motivic ring spectrum representing …
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Super symmetric vertex algebras and supercurves
… algebra V and a supercurve X, we construct a vector bundle [ ... ] on X, the fiber of which, is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that …
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Aspects of Generalized Geometry: Branes with Boundary, Blow-ups, Brackets and Bundles
… Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this …
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Projective Geometry for Perfectoid Spaces
… analog of projective space correspond to line bundles on X together with some extra data, reflecting the classical theory. Along the way we give a complete classification of vector bundles on the perfectoid unit disk, and compute the Picard group of the perfectoid analog of projective space.
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WEIGHT STRUCTURES AND MOTIVIC COMPARISONS OF P-ADIC COHOMOLOGY THEORIES FOR RIGID ANALYTIC SPACES
… that, for adic étale motives over C_p, the vector bundles on the Fargues--Fontaine curve arising from their Hyodo--Kato cohomology coincide with their de Rham--Fargues--Fontaine cohomology. The latter provides an overconvergent refinement of crystalline vector bundles, albeit constructed on …
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