Summands of theta divisors on Jacobians

Abstract

We show that the only summands of theta divisors on Jacobians of curves and on intermediate Jacobians of cubic threefolds are the obvious powers of the curve and the Fano surface of lines on the threefold. The proof uses the decomposition theorem for perverse sheaves, a bit of representation theory and a computation of characteristic cycles for Brill-Noether sheaves.

references updated, background on fiber functors and lambda rings added, proof of 2.5 made self-contained

References in corpus (2)

• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• Generic vanishing and minimal cohomology classes on abelian fivefolds

Cited by in corpus (1)

• Characteristic cycles and the microlocal geometry of the Gauss map, II