On the Schottky problem for genus five Jacobians with a vanishing theta null
We give a solution to the weak Schottky problem for genus-five Jacobians with a vanishing theta-null, answering a question of Grushevsky and Salvati Manni. More precisely, we show that if a principally polarized Abelian variety of dimension five has a vanishing theta-null with a quadric tangent cone of rank at most three, then it is in the Jacobian locus, up to extra irreducible components. We employ a degeneration argument, together with a study of the ramification loci for the Gauss map of a theta divisor.
© 2021 Scuola Normale Superiore. Submitted: Sep 25, 2019; Accepted: Nov 11, 2019; Published: Mar 30, 2021.
Submitted - 1905.09366.pdf