Generic vanishing and minimal cohomology classes on abelian fivefolds

We classify generic vanishing subschemes of principally polarised abelian varieties in dimension five, showing that they exist only on Jacobians of curves and intermediate Jacobians of cubic threefolds, and confirming a conjecture of Pareschi and Popa in this case. Our result is implied by a more general statement about subvarieties of minimal cohomology class whose sum is a theta divisor. This is joint work with Casalaina-Martin and Popa.