Generic vanishing and minimal cohomology classes on abelian fivefolds

Abstract

We classify GV-subschemes of five-dimensional ppavs, showing that they exist only on Jacobians of curves and intermediate Jacobians of cubic threefolds, and confirming a conjecture of Pareschi--Popa in this case. The result is implied by a more general statement about subvarieties of minimal cohomology class whose sum is a theta divisor.

23 pages; final version, to appear in J. Algebraic Geom

References in corpus (1)

• Decomposable theta divisors and generic vanishing

Cited by in corpus (2)

• Characteristic cycles and the microlocal geometry of the Gauss map, II
• Summands of theta divisors on Jacobians