Related papers: Effective vanishing theorems for ample and globall…

Let $p:\sXS$ be a proper K\"ahler fibration and $\sE\sX$ a Hermitian holomorphic vector bundle. As motivated by the work of Berndtsson(\cite{Berndtsson09a}), by using basic Hodge theory, we derive several general curvature formulas for the…

We study the bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors.…

Heterotic compactifications on Calabi-Yau threefolds frequently exhibit textures of vanishing Yukawa couplings in their low energy description. The vanishing of these couplings is often not enforced by any obvious symmetry and appears to be…

For a curve $C$ of genus $6$ or $8$ and a torsion bundle $\eta$ of order $\ell$ we study the vanishing of the space of global sections of the twist $E_C \otimes \eta$ of the rank two Mukai bundle $E_C$ of $C$. The bundle $E_C$ was used in a…

We establish a relative version of the abstract "affine representability" theorem in ${\mathbb A}^1$--homotopy theory from Part I of this paper. We then prove some ${\mathbb A}^1$--invariance statements for generically trivial torsors under…

We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on the n-dimensional projective space in terms of the vanishing of the cohomology of the factors. For this purpose we introduce regularity indices…

We propose a new class of filtered vector bundles, which is related to variation of (mixed) Hodge structures and give a slight generalization of the Fujita--Zucker--Kawamata semipositivity theorem.

We use the toric degeneration of Bott-Samelson varieties and the description of cohomolgy of line bundles on toric varieties to deduce vanishings results for the cohomology of lines bundles on Bott-Samelson varieties.

Quantum homogeneous vector bundles are introduced by a direct description of their sections in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies inherited from the quantum groups, and their sections…

In this article we study a special class of vector bundles, called tensors. A tensor consists of a vector bundle $E$ over a smooth irreducible projective variety and a morphism of vector bundles $\varphi$. As for classical vector bundles,…

The purpose of this note is to extend some classical results on quasi-projective schemes to the setting of derived algebraic geometry. Namely, we want to show that any vector bundle on a derived scheme admitting an ample line bundle can be…

A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale…

A Lie algebroid is a generalization of Lie algebra that provides a general framework to describe the symmetries of a manifold. In this paper, we generalize the Kodaira vanishing theorem, which is a basic result in complex geometry, to…

We consider the assembly map for principal bundles with fiber a countable discrete group. We obtain an index-theoretic interpretation of this homomorphism by providing a tensor-product presentation for the module of sections associated to…

In this paper, we give a simple proof of the Gauss-Bonnet-Chern theorem for a real oriented Finsler vector bundle with rank equal to the dimension of the base manifold. As an application, a Gauss-Bonnet-Chern formula for any…

We show that an equivariant vector bundle on a complete toric variety is nef or ample if and only if its restriction to every invariant curve is nef or ample, respectively. Furthermore, we show that nef toric vector bundles have a…

Let C be a projective smooth curve of genus g> 1. Let E be a vector bundle of rank r on C. For each integer r'<r, associate to E the invariant s_{r'}(E)=r'deg(E)-rdeg(E') where E'is a subbundle of E of rank r' and maximal degree. For every…

We produce full strong exceptional collections consisting of vector bundles on the geometric invariant theory quotient of certain linear actions of a split reductive group $G$ of rank two. The vector bundles correspond to irreducible…

For a certain class of vector bundles E on abelian varieties A over local fields containing all line bundles algebraically equivalent to zero we define a canonical representation of the Tate module of A on the fibre of E in the zero…

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…