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In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation...
On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearl...
By proving an integral formula of the curvature tensor of EdetE, we observe that the curvature of EdetE is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Na...
Let p : X ! S be a smooth K¨ahler fibration and E ! X a Hermitian holomorphic vector bundle. As motivated by the work of Berdtsson([Bern09]), by using basic Hodge theory, we derive several general cur...
We give a cohomological classification of vector bundles on smooth affine threefolds over algebraically closed fields having characteristic unequal to 2. As a consequence, if A is a smooth affine alge...
Abstract: Over a scheme with 2 invertible, we show that a vector bundle of rank four has a sub or quotient line bundle if and only if the canonical symmetric bilinear form on its exterior square has a...
Abstract: We study a filtered generalization of the operation of elementary modification of vector bundles. The generalization is motivated by applications to the degeneration theory of linear systems...
We consider the moduli space of stable vector bundles on curves embedded in P2 with Hilbert polynomial 3m+ 1 and construct a compactification of this space by vector bundles. The result fM is a blow u...
Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of pa...
The purpose of this paper is to give necessary and sufficient conditions for the orientability of vector bundles over flag manifolds of real semi-simple Lie groups. We focus on two kinds of vector bun...
A recollement of vector bundles     vector bundles  math       2010/11/24
For a weighted projective line, the stable category of its vector bundles modulo lines bundles has a natural triangulated structure. We prove that, for any positive integers $p, q, r$ and $r'$ with $r...
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Here we prove that for a smooth projective variety $X$ of arbitrary dimension and for a vector bundle $E$ over $X$, the Harder-Narasimhan filtration of a Frobenius pull back of $E$ is a refinement of...
If a sequence of Riemannian manifolds, $X_i$, converges in the pointed Gromov-Hausdorff sense to a limit space, $X_\infty$, and if $E_i$ are vector bundles over $X_i$ endowed with metrics of Sasaki-t...
Let Y be a normal and projective variety over an algebraically closed field k and V a vector bundle over Y . We prove that if there exist a k-scheme X and a finite surjective morphism g : X → Y that t...

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