Related papers: Splitting criterion for reflexive sheaves

Let H be a closed subgroup of a linear algebraic group G defined over a field F. There is an equivalence of categories between the category of linear finite-dimensional representations of H and the category of finite rank G-homogeneous…

We introduce a new method to study mixed characteristic deformation of line bundles. In particular, for sufficiently large smooth projective families $f : \mathscr{X} \to \mathscr{S}$ defined over the ring of $N$-integers…

Let $R$ be an excellent Henselian discrete valuation ring with algebraically closed residue field $k$ of any characteristic. Fix integers $r,d$ with $r\ge 2$. Let $X_R$ be a regular fibred surface over Spec($R$) with special fibre denoted…

Let X be a 1-connected compact space such that the algebra H*(X;Z/2) is generated by one single element. We compute the cohomology of the free loop space H*(LX;Z/2) including the Steenrod algebra action. When X is a projective space CP^n,…

A ribbon is a first-order thickening of a non-singular curve. Motivated by a question of Eisenbud and Green, we show that a compactification of the moduli space of line bundles on a ribbon is given by the moduli space of semi-stable…

This paper investigates the cohomological property of vector bundles on biprojective space. We will give a criterion for a vector bundle to be isomorphic to the tensor product of pullbacks of exterior products of differential sheaves.

We prove a Horrocks-type splitting criterion for arbitrary smooth projective toric varieties under an additional hypothesis similar to the case of products of projective spaces by Eisenbud--Erman--Schreyer.

We show that Horrocks' criterion for the splitting of rank two vector bundles in P^3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P^4. Extension of other splitting criterion are studied.

This paper classifies all the tilting bundles in the category of coherent sheaves on the weighted projective line of weight type $(2, 2, n)$, and investigates the abelianness of the "missing part" from the category of coherent sheaves to…

This is an expository article. In the first part we recall the definition and a few results concerning singular Hermitian metrics on torsion-free coherent sheaves. They offer the perfect platform for the study of properties of direct images…

The paper consists of three parts. In the first of them different kinds stability are discussed. In particular, the stability concept with respect to nef divisor is introduced. A structure of rigid and superrigid vector bundles on smooth…

We introduce a notion of regularity for coherent sheaves on Grassmannians of lines. We use this notion to prove some extension of Evans-Griffith criterion to characterize direct sums of line bundles. We also give a cohomological…

We construct vector bundles $R^r_\mu$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $\iff$ $Hom(R^r_\mu,E)=0$. As a…

According to the decomposition and relative hard Lefschetz theorems, given a projective map of complex quasi projective algebraic varieties and a relatively ample line bundle, the rational intersection cohomology groups of the domain of the…

We give an algorithm to determine whether a kernel sheaf over a smooth projective curve over an algebraically closed field is semistable. The algorithm uses symmetric powers to make destabilizing subbundles visible as global sections.

We find the sharp bounds on $h^0(F)$ for one-dimensional semistable sheaves $F$ on a projective variety $X$ by using the spectrum of semistable sheaves. The result generalizes the Clifford theorem. When $X$ is the projective plane…

We address the question of existence of sections of fibrations in two settings. First, we show that a bundle with base a finite 2-complex admits a section if and only if the inclusion of the fiber is $\pi_1$-injective and the associated…

Grothendieck proved that any locally free sheaf on a projective line over a field (uniquely) decomposes into a direct sum of line bundles. Ishii and Uehara construct an analogue of Grothendieck's theorem for pure sheaves on the fundamental…

We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived…

A ribbon is a non-reduced curve modelled on the first infinitesimal neighbourhood of a smooth curve in a surface. This paper is devoted to describe some properties of coherent sheaves on such a curve and their Simpson moduli space. In…