On the Schottky problem for genus five Jacobians with a vanishing theta null

2019/05/22 by Agostini, Daniele, Chua, Lynn
#14H40 #14H42 #14K10 #14K25 #14Q99 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.09366

Abstract

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.

Related

• Jacobians with a vanishing theta-null in genus 4
• The Tannakian Schottky Conjecture in Genus Five
• The degree of the Jacobian locus and the Schottky problem
• An explicit solution to the weak Schottky problem
• The Schottky Problem