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arXiv · 1905.09366

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

Daniele Agostini·Lynn Chua
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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.

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Daniele Agostini, Lynn Chua. 2019-05-22. On the Schottky problem for genus five Jacobians with a vanishing theta null. https://arxiv.org/abs/1905.09366

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