On Border Basis and Gröbner Basis Schemes.
On deformation of maximally degenerate stable marked curves and Oda's problem.
On Deformations of Threedimensional Rational Manifolds.
On Donaldson polynomials of rational ruled surfaces.
On Moduli of Algebraic Varieties. I.
On moduli of algebraic varieties II
On moduli of algebraic varieties III. Fine moduli spaces
On moduli of -bundles of a curve for exceptional
On moduli spaces of semistable sheaves on Enriques surfaces
We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In the case of a nodal Enriques surface the moduli spaces obtained are reducible for general polarizations. For unnodal Enriques surfaces we show how to reduce the study of moduli spaces of high even rank Gieseker semistable sheaves to low ranks. To prove this we use the method of K. Yoshioka who showed that in the odd rank case, one can reduce to rank...
On Newstaed' s conjecture on vector bundles on algebraic curves.
On Picard bundles over Prym varieties.
On Postulation of Curves in IP4.
On representation varieties of Artin groups, projective arrangements and the fundamental groups of smooth complex algebraic varieties
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 Cohomology Groups of Moduli Spaces of Vector Bundles on Curves.
On the components of moduli of simple sheaves on a surface.
On the geometry of moduli of curves and line bundles
Here we focus on the geometry of , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into and we give generators and relations of the rational Picard group of , extending previous work by A. Kouvidakis.
On the Graded Ring of Hubert Modular Forms Associated with Q (|..5).
On the Hilbert Scheme of Curves in Higher-dimensional Projective Space.
On the Kodaira Dimension of the Moduli Space of Curves.