On the Kodaira dimension of the moduli space of curves, II. The even-genus case.
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 motives of moduli of chains and Higgs bundles
We take another approach to Hitchin’s strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle action. Our computation is done in the dimensional completion of the Grothendieck ring of varieties and starts by describing the classes of moduli stacks of chains rather than their coarse moduli spaces. As an application we show that the -torsion of the Jacobian acts trivially on the middle dimensional cohomology of the moduli space of twisted...
On the Periods of Enriques Surfaces. I.
On the reducibility of moduli spaces of stable 2-bundles over an elliptic surface.
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 the stratification of the moduli space of Mumford curves
On the tautological ring of Mg.
Ordinariness in good reductions of Shimura varieties of PEL-type
Orthogonal bundles on curves and theta functions
Let be the moduli space of principal -bundles on a curve , and the determinant bundle on . We define an isomorphism of onto the dual of the space of -th order theta functions on the Jacobian of . This isomorphism identifies the rational map defined by the linear system with the map which associates to a quadratic bundle the theta divisor . The two components and of are mapped into the subspaces of even and odd theta functions respectively. Finally we discuss the analogous...