On the components of moduli of simple sheaves on a surface.
On the discriminant variety of a projective manifold.
on the existence of stable rank-2 sheaves on algebraic surfaces
On the Horizontal Base Locus of Multiples of Tautological Sheaves of Projectived Cotangent Bundles, II.
On the moduli of reflexive sheaves on a surface with rational double points.
On the moduli of stable vector bundles on a Hirzebruch surface.
On the normal bundle of an exceptional curve in a higher dimensional algebraic manifold.
On the preservation of k-very ampleness under adjunction.
On the principal bundles over a flag manifold.
On the second sectional geometric genus of quasi-polarized manifolds.
On the S-fundamental group scheme
We introduce a new fundamental group scheme for varieties defined over an algebraically closed (or just perfect) field of positive characteristic and we use it to study generalization of C. Simpson’s results to positive characteristic. We also study the properties of this group and we prove Lefschetz type theorems.
On the stability of the tangent bundle of Fano manifolds.
On the strange duality conjecture for abelian surfaces
We study Le Potier's strange duality conjecture for moduli spaces of sheaves over generic abelian surfaces. We prove the isomorphism for abelian surfaces which are products of elliptic curves, when the moduli spaces consist of sheaves of equal ranks and ber degree 1. The birational type of the moduli space of sheaves is also investigated. Generalizations to arbitrary product elliptic surfaces are given.
On vector bundles whose general sections have all projectively equivalent zero-loci
On Verlinde sheaves and strange duality over elliptic Noether-Lefschetz divisors
We extend results on generic strange duality for surfaces by showing that the proposed isomorphism holds over an entire Noether-Lefschetz divisor in the moduli space of quasipolarized s. We interpret the statement globally as an isomorphism of sheaves over this divisor, and also describe the global construction over the space of polarized .
Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface (II).
In [6], orbifold G-bundles on a certain class of elliptic fibrations over a smooth complex projective curve X were related to parabolic G-bundles over X. In this continuation of [6] we define and investigate holomorphic connections on an orbifold G-bundle over an elliptic fibration.
Osculatory behavior and second dual varieties of Del Pezzo surfaces.