On moduli of algebraic varieties II
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...
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...
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.
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...