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On Ampleness of vector bundles [PDF]
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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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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Acta Mathematica Sinica, English Series, 2014 In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term
Zhuo Chen
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Vector Bundles with No Soul [PDF]
Proceedings of the American Mathematical Society, 1994 We exhibit vector bundles over compact manifolds of nonnegative sectional curvature whose total spaces do not admit a complete metric of nonnegative sectional curvature.
Özaydin, Murad, Walschap, Gerard
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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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\'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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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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The vector bundle decomposition [PDF]
Pacific Journal of Mathematics, 2003 The subject of this paper is the question whether a given vector bundle can be decomposed (or split) into a Whitney sum of its subbundles. The authors claim that in the real case the literature is sketchy at best (the reviewer will comment on this below), and they continue: ``In this paper we shall begin the study of the decomposition of real vector ...
Leslie, Joshua A., Yue, Qingqi
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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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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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