Characteristic classes and Hilbert-Poincaré series for perverse sheaves on abelian varieties

Abstract

The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational function of a very simple shape and that a similar result holds for the symmetric convolution powers. We also give formulae for other Schur functors in terms of characteristic classes on the dual abelian variety, and as an example we discuss the case of Prym-Tjurin varieties.

Some typos removed, references updated

References in corpus (5)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Perverse sheaves on semiabelian varieties
• On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety
• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• On a family of surfaces of general type attached to abelian fourfolds and the Weyl group W(E_6)