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Approximate and discrete Euclidean vector bundles
Forum of Mathematics, Sigma, 2023 We introduce $\varepsilon $ -approximate versions of the notion of a Euclidean vector bundle for $\varepsilon \geq 0$ , which recover the classical notion of a Euclidean vector bundle when $\varepsilon = 0$ .
Luis Scoccola, Jose A. Perea
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On Ampleness of vector bundles
Comptes Rendus. Mathématique, 2021 In this article, we give a necessary and sufficient condition for ampleness of semistable vector bundles with vanishing discriminant on a smooth projective variety $X$.
Misra, Snehajit, Ray, Nabanita
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Root bundles and towards exact matter spectra of F-theory MSSMs
Journal of High Energy Physics, 2021 Motivated by the appearance of fractional powers of line bundles in studies of vector-like spectra in 4d F-theory compactifications, we analyze the structure and origin of these bundles.
Martin Bies +4 more
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Limits of the trivial bundle on a curve [PDF]
Épijournal de Géométrie Algébrique, 2018 We attempt to describe the rank 2 vector bundles on a curve C which are specializations of the trivial bundle. We get a complete classifications when C is Brill-Noether generic, or when it is hyperelliptic; in both cases all limit vector bundles are ...
Arnaud Beauville
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\'Etale triviality of finite equivariant vector bundles [PDF]
Épijournal de Géométrie Algébrique, 2021 Let H be a complex Lie group acting holomorphically on a complex analytic space X such that the restriction to X_{\mathrm{red}} of every H-invariant regular function on X is constant.
Indranil Biswas, Peter O'Sullivan
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Fibonacci, Golden Ratio, and Vector Bundles
Mathematics, 2021 There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra
Noah Giansiracusa
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Automorphic vector bundles on the stack of G-zips
Forum of Mathematics, Sigma, 2021 For a connected reductive group G over a finite field, we study automorphic vector bundles on the stack of G-zips. In particular, we give a formula in the general case for the space of global sections of an automorphic vector bundle in terms of the ...
Naoki Imai, Jean-Stefan Koskivirta
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Mirror symmetry for Nahm branes [PDF]
Épijournal de Géométrie Algébrique, 2022 The Dirac--Higgs bundle is a hyperholomorphic bundle over the moduli space of stable Higgs bundles of coprime rank and degree. We provide an algebraic generalization to the case of trivial degree and the rank higher than $1$.
Emilio Franco, Marcos Jardim
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Vector Bundles on the Moduli Stack of Elliptic Curves [PDF]
, 2015 We study vector bundles on the moduli stack of elliptic curves over a local ring R. If R is a field or a discrete valuation ring of (residue) characteristic not 2 or 3, all these vector bundles are sums of line bundles.
Bauer +28 more
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Topological insulators and geometry of vector bundles
SciPost Physics Lecture Notes, 2023 For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information.
Alexadner S. Sergeev
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