Related papers: A Few Splitting Criteria for Vector Bundles

The purpose of this paper is to study an extended version of bivariant derived algebraic cobordism where the cycles carry a vector bundle on the source as additional data. We show that, over a field of characteristic 0, this extends the…

Given a vector bundle $E$ on a tree of smooth rational curves $C$, we give necessary and sufficient conditions for a vector bundle $E'$ on $\mathbb{P}^1$ to specialize to $E$ on $C$, generalizing the rank 2 case, due to Coskun.

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…

We are concerned with the problem of the stability of the syzygy bundles associated to base point free vector spaces of forms of the same degree d on the projective space of dimension n. We deduce directly, from Mark Green's vanishing…

We consider the problem of determining all pairs (c_1, c_2) of Chern classes of rank 2 bundles that are cokernel of a skew-symmetric matrix of linear forms in 3 variables, having constant rank 2c_1 and size 2c_1+2. We completely solve the…

We introduce the notion of a generalized intersection pairing for an Artin stack with a proper good moduli space and nonempty stable part. For the moduli stack of semistable bundles over a smooth projective curve, there are four known…

Let $C$ be a curve and $V \to C$ an orthogonal vector bundle of rank $r$. For $r \le 6$, the structure of $V$ can be described using tensor, symmetric and exterior products of bundles of lower rank, essentially due to the existence of…

Let E and F be vector bundles over a complex projective smooth curve X, and suppose that 0 -> E -> W -> F -> 0 is a nontrivial extension. Let G be a subbundle of F, and D an effective divisor on X. We give a criterion for the subsheaf G(-D)…

A family of holomorphic vector bundles is constructed on a complex manifold $X$. The space of the holomorphic sections of these bundles are calculated in certain cases. As an application, if $X$ is an $N$-dimensional compact K\"ahler…

We provide several results on splice-quotient singularities: a combinatorial expression of the dimension of the first cohomology of all `natural' line bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the dimension of…

We develop a semistability algorithm for vector bundles which are given as a kernel of a surjective morphism between splitting bundles on the projective space over an algebraically closed field K. This class of bundles is a generalization…

In this article we describe vector bundles over projectivoid line and show how it is similar to (and different) from Gorthendieck's classification of vector bundles over projective line.

Let $X$ be a compact Riemann surface. A quadratic pair on $X$ consists of a holomorphic vector bundle with a quadratic form which takes values in fixed line bundle. We show that the moduli spaces of quadratic pairs of rank 2 are connected…

In this article we announce some results on compactifying moduli spaces of rank-2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so called bubbling of vector…

We discuss the relationship between the ${\mathbb A}^1$-homotopy sheaves of ${\mathbb A}^n \setminus 0$ and the problem of splitting off a trivial rank $1$ summand from a rank $n$-vector bundle. We begin by computing $\pi_3^{{\mathbb…

Different techniques from machine learning are applied to the problem of computing line bundle cohomologies of (hypersurfaces in) toric varieties. While a naive approach of training a neural network to reproduce the cohomologies fails in…

This work revolves around the question of whether a given resonance variety is associated with a vector bundle. We show the existence of a family of natural morphisms on a stratification of the resonance variety to a suitable family of a…

Quadric bundles on a compact Riemann surface X generalise orthogonal bundles and arise naturally in the study of the moduli space of representations of $\pi_1(X)$ in Sp(2n,R). We prove some basic results on the moduli spaces of quadric…

Let $C$ be a curve of genus two. We denote by $SU_C(3)$ the moduli space of semi-stable vector bundles of rank 3 and trivial determinant over $C$, and by $J^d$ the variety of line bundles of degree $d$ on $C$. In particular, $J^1$ has a…

In this note we consider the moduli space of stable bundles of rank two on a very general quintic surface. We study the potentially obstructed points of the moduli space via the spectral covering of a twisted endomorphism. This analysis…