Related papers: Common subbundles and intersections of divisors

In the holomorphic or algebraic setting we consider a vector bundle E on a smooth subvariety X in a smooth variety Y over a field of characteristic zero. Assuming E extends to the l-th neighborhood of X in Y, we study cohomological…

This paper gives a uniform, self-contained and direct approach to a variety of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give necessary and sufficient cohomological criteria for the existence of various…

Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…

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 formulate a tropical analogue of Grothendieck's section conjecture: that for every stable graph G of genus g>2, and every field k, the generic curve with reduction type G over k satisfies the section conjecture. We prove many cases of…

Let $X$ be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of $X$ is ample. Using the cylinder homomorphism associated with the family of complete…

In the first part of this paper, we propose a uniform interpretation of characteristic classes as obstructions to the reduction of the structure group and to the existence of an equivariant extension of a certain homomorphism defined a…

We study the deformation-obstruction theory of Koszul cohomology groups of $g^r_d$'s on singular nodal curves. We compute the obstruction classes for Koszul cohomology classes on singular curves to deform to a smooth one. In the case the…

The aim of this paper is to study the cohomology theory of monoid schemes in general and apply it to vector and line bundles. We will prove that over separated monoid schemes, any vector bundle is a coproduct of line bundles and then go on…

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…

This paper begins with a description of cohomological invariants of non-degenerate quadric bundles, in terms of the cohomology rings of the classifying spaces of the general orthogonal groups. Following this, the Main Theorem of the paper…

The classical BKK theorem computes the intersection number of divisors on toric variety in terms of volumes of corresponding polytopes. It was observed by Pukhlikov and the first author that the BKK theorem leads to a presentation of the…

Any arrangement of hyperplanes in general position in $P^n$ can be regarded as a divisor with normal crossing. We study the bundles of logarithmic 1-forms corresponding to such divisors` from the point of view of classification of vector…

It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several…

This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and show…

Let $G$ be a locally semisimple ind-group, $P$ be a parabolic subgroup, and $E$ be a finite-dimensional $P$-module. We show that, under a certain condition on $E$, the nonzero cohomologies of the homogeneous vector bundle…

This paper presents a gentle introduction to cohomology vanishing theorems, largely based on the paper work of Hongshan Li. It offers an insightful exploration of unitary local systems on complex manifolds, particularly focusing on their…

In this paper, we study the cohomology of vector bundles on projective space defined as kernels or cokernels of general maps $V_1 \to V_2$, where the $V_i$ are direct sums of line bundles or certain exceptional bundles. We prove an…

For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of…

Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of…