Moduli spaces of stable sheaves on abelian surfaces

In this paper, we consider basic problems on moduli spaces of stable sheaves on abelian surfaces. Our main assumption is the primitivity of the associated Mukai vector. We determine the deformation types, albanese maps, Bogomolov factors and their weight 2 Hodge structures. We also discuss the deformation types of moduli spaces of stable sheaves on K3 surfaces. Received: 28 February 2000 / Revised version: 15 September 2000 / Published online: 24 September 2001