Bundles of generalized theta functions over abelian surfaces

Abstract

We study the 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 Drezet-Narasimhan from curves to abelian surfaces.

References in corpus (1)

• Cohomology of the Hilbert scheme of points on a surface with values in representations of tautological bundles

Cited by in corpus (1)

• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories