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arXiv · 1409.3134

Theta divisors with curve summands and the Schottky problem

Stefan Schreieder
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Abstract

We prove the following converse of Riemann's Theorem: let (A,Θ) be an indecomposable principally polarized abelian variety whose theta divisor can be written as a sum of a curve and a codimension two subvariety Θ=C+Y. Then C is smooth, A is the Jacobian of C, and Y is a translate of W_{g-2}(C). As applications, we determine all theta divisors that are dominated by a product of curves and characterize Jacobians by the existence of a d-dimensional subvariety with curve summand whose twisted ideal sheaf is a generic vanishing sheaf.

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Stefan Schreieder. 2015-08-25. Theta divisors with curve summands and the Schottky problem. https://doi.org/10.1007/s00208-015-1287-8

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