Bundles of generalized theta functions over abelian surfaces

Abstract

We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree $0$, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier–Mukai symmetries of the Verlinde bundles are found consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drézet–Narasimhan from curves to abelian surfaces.