Related papers: Stable toric sheaves. I : Chern classes

Let $X$ be a nonsingular complex projective variety and $D$ a locally quasi-homogeneous free divisor in $X$. In this paper we study a numerical relation between the Chern class of the sheaf of logarithmic derivations on $X$ with respect to…

In this note, we report on a work jointly done with C. Simpson on a generalization of Reznikov's theorem which says that the Chern-Simons classes and in particular the Deligne Chern classes (in degrees $> 1$) are torsion, of a flat vector…

This paper gives an explicit computation of the category of constructible sheaves on a toric variety (with respect to the stratification by torus orbits). Over the complex numbers, this simplifies a description due to Braden and Lunts. The…

In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of coherent sheaves. This method also allows us to derive a…

We compute the expected dimension of the moduli space of torsion-free rank 2 sheaves at a point corresponding to a stable reflexive sheaf and give conditions for the existence of a perfect tangent-obstruction complex on a class of smooth…

Let $X \subset Y$ be closed (possibly singular) subschemes of a smooth projective toric variety $T$. We show how to compute the Segre class $s(X,Y)$ as a class in the Chow group of $T$. Building on this, we give effective methods to compute…

Given a reflexive sheaf on a mildly singular projective variety, we prove a flatness criterion under certain stability conditions. This implies the algebraicity of leaves for sufficiently stable foliations with numerically trivial canonical…

We employ combinatorial techniques to present an explicit formula for the coefficients in front of Chern classes involving in the Hattori-Stong integrability conditions. We also give an evenness condition for the signature of stably…

Any toric flip naturally induces an equivalence between the associated categories of equivariant reflexive sheaves, and we investigate how slope stability behaves through this functor. On one hand, for a fixed toric sheaf, and natural…

For (X,L) a polarized toric variety and G a torus of automorphisms of (X,L), denote by Y the GIT quotient X/G. We define a family of fully faithful functors from the category of torus equivariant reflexive sheaves on Y to the category of…

We show that under some assumptions on the monodromy group some combinations of higher Chern classes of flat vector bundles are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles…

In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the explicit parametrisation of torsion free rank one sheaves on projective irreducible curves with vanishing cohomology…

Extending work of Klyachko, Perling and Kool we develop a combinatorial description of torsion free toric sheaves in any dimension on smooth toric DM stacks. We investigate their basic properties and under certain conditions recover some…

In this paper, we prove a generalization of Reznikov's theorem which says that the Chern-Simons classes and in particular the Deligne Chern classes (in degrees $>1$) are torsion, of a flat bundle on a smooth complex projective variety. We…

Summary: The Hodge conjecture asks whether rational Hodge classes on a smooth projective manifolds are generated by the classes of algebraic subsets, or equivalently by Chern classes of coherent sheaves. On a compact Kaehler manifold, Hodge…

We study equivariant resolutions and local cohomologies of toric sheaves for affine toric varieties, where our focus is on the construction of new examples of decomposable maximal Cohen-Macaulay modules of higher rank. A result of Klyachko…

We consider the moduli space of stable torsion free sheaves of any rank on a smooth projective threefold. The singularity set of a torsion free sheaf is the locus where the sheaf is not locally free. On a threefold it has dimension $\leq…

We provide a stacky fan description of the total space of certain split vector bundles, as well as their projectivization, over toric Deligne-Mumford stacks. We then specialize to the case of Hirzebruch orbifold $\mathcal{H}_{r}^{ab}$…

This paper extends a number of known results on slope-semistable sheaves from the classical case to the setting where polarisations are given by movable curve classes. As applications, we obtain new flatness results for reflexive sheaves on…

Assume that $X$ is a compact complex analytic variety which has quotient singularities in codimension 2, and that $\mathcal{F}$ is a reflexive sheaf on $X$. Using orbifold modifications, we can define first and second homological Chern…