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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：2-representations and 2-vector bundles
2 向量丛 群论
2023/4/13
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...
Effective vanishing theorems for ample and globally generated vector bundles
Effective vanishing theorems ample globally generated vector bundles
2018/4/19
By proving an integral formula of the curvature tensor of E⊗detE, we observe that the curvature of E⊗detE is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Na...
CURVATURES OF DIRECT IMAGE SHEAVES OF VECTOR BUNDLES AND APPLICATIONS
CURVATURES DIRECT IMAGE SHEAVES VECTOR BUNDLES APPLICATIONS
2018/4/19
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...
A cohomological classification of vector bundles on smooth affine threefolds
cohomological classification vector bundles smooth affine threefolds Algebraic Geometry
2012/4/23
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...
Modification of the Simpson moduli space M_{3m+1}(P_2) by vector bundles (I)
Modification Simpson moduli space M_{3m+1}(P_2) vector bundles (I)
2011/2/28
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...
Vector bundles of rank 2 computing Clifford indices
Semistable vector bundle Clifford indices gonality
2011/1/17
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...
Orientability of vector bundles over real flag manifolds
Vector bundles Orientability Flag manifold
2011/1/17
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...
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
elliptic curves the associative Yang-Baxter equation
2010/11/23
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...
Convergence of vector bundles with metrics of Sasaki-type
Convergence vector bundles metrics of Sasaki-type
2010/11/9
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...
Vector Bundles over Normal Varieties Trivialized by Finite Morphisms
Essentially finite vector bundles finite mor-phisms principal bundles
2010/12/13
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...