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We construct examples of non-isomorphic algebraic vector bundles on the punctured affine space with isomorphic pullbacks to the smooth quadric.

Group Theory · Mathematics 2013-03-05 Brent Doran , Jun Yu

Let G be a compact, connected and simply connected Lie group, and {\Omega}G the space of the loops in G based at the identity. This note shows a way to compute the cohomology of the total space of a principal {\Omega}G-bundle over a…

Algebraic Topology · Mathematics 2013-09-26 Samuel Tinguely

A flat vector bundle on an algebraic variety supports two natural definable structures given by the flat and algebraic coordinates. In this note we show these two structures coincide, subject to a condition on the local monodromy at…

Algebraic Geometry · Mathematics 2022-01-07 Benjamin Bakker , Scott Mullane

In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we study the $\alpha$-structure of frame bundles over…

Differential Geometry · Mathematics 2014-04-29 Didong Li , Huafei Sun , Chen Tao , Lin Jiu

A theory of principal bundles possessing quantum structure groups and classical base manifolds is presented. Structural analysis of such quantum principal bundles is performed. A differential calculus is constructed, combining differential…

q-alg · Mathematics 2009-10-28 Mico Durdevic

We classify all isomorphisms between moduli stacks of vector bundles of fixed determinant on a smooth complex projective of genus at least 4. It is shown that each isomorphism between two different moduli stacks can be described as a…

Algebraic Geometry · Mathematics 2025-11-26 David Alfaya , Indranil Biswas , Tomás L. Gómez

We study flat vector bundles over complex parallelizable manifolds.

Algebraic Geometry · Mathematics 2009-09-25 Jörg Winkelmann

We characterize the vector bundles on G(1,4) that have no intermediate cohomology. We obtain them from extensions of the universal bundles and others related with them. In particular, we get a characterization of the universal vector…

Algebraic Geometry · Mathematics 2007-05-23 Enrique Arrondo , Beatriz Grana

We study certain moduli spaces of stable vector bundles of rank two on cubic and quartic threefolds. In many cases under consideration, it turns out that the moduli space is complete and irreducible and a general member has vanishing…

Algebraic Geometry · Mathematics 2008-04-21 Indranil Biswas , Jishnu Biswas , G. V. Ravindra

We prove that the tangent bundle of a generic space of planar n-gons with specified side lengths, identified under isometry, plus a trivial line bundle is isomorphic to (n-2) times a canonical line bundle. We then discuss consequences for…

Algebraic Topology · Mathematics 2018-05-09 Donald M. Davis

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article…

Differential Geometry · Mathematics 2007-05-23 Scott Morrison

In this paper we give some properties of the algebraic and geometric structure of the endomorphisms monoid of a homogeneous vector bundle.

Algebraic Geometry · Mathematics 2013-10-10 L. Brambila-Paz , Alvaro Rittatore

A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…

q-alg · Mathematics 2008-02-03 Mico Durdevic

We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle $E\rightarrow M$, over a Riemannian manifold $M$, when $E$ is endowed with a…

Differential Geometry · Mathematics 2017-02-28 Rui Albuquerque

We prove an existence result for stable vector bundles with arbitrary rank on an algebraic surface, and determine the birational structure of certain moduli space of stable bundles on a rational ruled surface.

Algebraic Geometry · Mathematics 2016-09-06 Wei-ping Li , Zhenbo Qin

The algebraic approach to bundles in non-commutative geometry and the definition of quantum real weighted projective spaces are reviewed. Principal U(1)-bundles over quantum real weighted projective spaces are constructed. As the spaces in…

Quantum Algebra · Mathematics 2012-07-11 Tomasz Brzeziński , Simon A. Fairfax

We study function theory and K\"ahler geometry on total spaces of vector bundles on an elliptic curve. For rank two vector bundles of degree zero, we show that any two total spaces are biholomorphic if and only if the corresponding vector…

Differential Geometry · Mathematics 2025-11-13 Hanyu Wu , Bo Yang

We define functorial isomorphisms of parallel transport along \'etale paths for a class of principal $G$-bundles on a $p$-adic curve. Here $G$ is a connected reductive algebraic group of finite presentation and the considered principal…

Algebraic Geometry · Mathematics 2007-06-08 Urs Hackstein

We investigate the analog of holomorphic vector bundles in the context of Sasakian manifolds.

Differential Geometry · Mathematics 2009-03-20 Indranil Biswas , Georg Schumacher

We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…

General Topology · Mathematics 2023-12-01 Takanobu Aoyama