On relative canonical sheaves of arithmetic surfaces.
On the 2 Very Ampleness of the Adjoint Bundle.
On the adjunction mapping for surfaces of Kodaira dimension ... 0 in Char.p.
On the adjunction theoretic classification of polarized varieties.
On the boundedness of the set of ample vector bundles with fixed sectional genus
On the Brill-Noether theory for K3 surfaces
Let (S, H) be a polarized K3 surface. We define Brill-Noether filtration on moduli spaces of vector bundles on S. Assume that (c 1(E), H) > 0 for a sheaf E in the moduli space. We give a formula for the expected dimension of the Brill-Noether subschemes. Following the classical theory for curves, we give a notion of Brill-Noether generic K3 surfaces. Studying correspondences between moduli spaces of coherent sheaves of different ranks on S, we prove our main theorem: polarized K3 surface which...
On the cohomological strata of families of vector bundles on algebraic surfaces
In this Note we study certain natural subsets of the cohomological stratification of the moduli spaces of rank vector bundles on an algebraic surface. In the last section we consider the following problem: take a bundle given by an extension, how can one recognize that is a certain given bundle? The most interesting case considered here is the case since it applies to the study of codimension meromorphic foliations with singularities on .
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.