Related papers: Generically nef vector bundles on ruled surfaces

We show that when a K3 surface acquires a node, the existence of stable spherical sheaves of certain Chern classes can be obstructed.

We consider the inhomogeneous div-curl system (i.e.\ to find a vector field with prescribed div and curl) in a bounded star-shaped domain in $\mathbb{R}^3$. An explicit general solution is given in terms of classical integral operators,…

We define a Chern--Simons invariant of connections on stably trivial vector bundles over smooth manifolds, taking values in $3$-forms modulo closed forms with integral cohomology class. We show an additivity property of this invariant for…

We desribe vector bundles over a class of noncommutative curves, namely, over noncommutative nodal curves of string type and of almost string type. We also prove that in other cases the classification of vector bundles over a noncommutative…

The Mehta-Ramanathan theorem ensures that the restriction of a stable vector bundle to a sufficiently high degree complete intersection curve is again stable. We improve the bounds for the "sufficiently high degree" and propose a possibly…

We give an upper bound for the maximal slope of the tensor product of several non-zero Hermitian vector bundles on the spectrum of an algebraic integer ring. By Minkowski's theorem, we need to estimate the Arakelov degree of an arbitrary…

We study the behaviour of semistability under tensor product in various settings: vector bundles, euclidean and hermitian lattices (alias Humbert forms or Arakelov bundles), multifiltered vector spaces. One approach to show that semistable…

The main goal of this paper is to generalize a part of the relationship between mean curvature and Harder-Narasimhan filtrations of holomorphic vector bundles to arbitrary polarized fibrations. More precisely, for a polarized family of…

Severi varieties and Brill-Noether theory of curves on K3 surfaces are well understood. Yet, quite little is known for curves on abelian surfaces. Given a general abelian surface $S$ with polarization $L$ of type $(1,n)$, we prove…

The goal of this paper is to make a surprising connection between several central conjectures in algebraic geometry: the Nonvanishing Conjecture, the Abundance Conjecture, and the Semiampleness Conjecture for nef line bundles on K-trivial…

Let $X$ be a K3 surface with Picard group $\mathrm{Pic}(X)\cong\mathbb{Z} H$ such that $H^2=2n$. Let $M_{H}(\mathbf{v})$ be the moduli space of Gieseker semistable sheaves on $X$ with Mukai vector $\mathbf{v}$. We say that $\mathbf{v}$…

We study vector bundles on flag varieties over an algebraically closed field $k$. In the first part, we suppose $G=G_k(d,n)$ $(2\le d\leq n-d)$ to be the Grassmannian manifold parameterizing linear subspaces of dimension $d$ in $k^n$, where…

We give a cohomological criterion for a parabolic vector bundle on a curve to be semistable. It says that a parabolic vector bundle $E$ with rational parabolic weights is semistable if and only if there is another parabolic vector bundle…

A family of curves over a discrete valuation ring is called semi-factorial if every line bundle on the generic fibre extends to a line bundle on the total space. In the nodal case, we give a sufficient and necessary condition for…

If $\P^\infty$ is the projective ind-space, i.e. $\P^\infty$ is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on $\P^\infty$ is…

In this paper, we give a simple proof of a triviality criterion due to I.Biswas and J.Pedro and P.Dos Santos. We also prove a vector bundle on a homogenous space is trivial if and only if the restrictions of the vector bundle to Schubert…

For a vector bundle V over a curve X of rank n and for each integer r in the range 1 \le r \le n-1, the Segre invariant s_r is defined by generalizing the minimal self-intersection number of the sections on a ruled surface. In this paper we…

In this article we deduce criteria for the splitting and the triviality of vector bundles, by restricting them to partially ample divisors. This allows to study the problem of splitting on the total space of fibre bundles. The statements…

Let U(r) be the moduli space of rank r vector bundles with trivial determinant on a smooth curve of genus 2. The map theta_r: U(r) -> |r Theta|, which associates to a general bundle its theta divisor, is generically finite. In this paper we…

In this paper we prove restriction theorems for torsion-free sheaves that are (semi)stable with respect to the truncated Hilbert polynomial over a smooth projective variety. Our results apply in particular to Gieseker-semistable sheaves and…