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Theta divisors with curve summands and the Schottky problem

Stefan Schreieder

Number 8
Author Stefan Schreieder
Year 2014

We prove the following converse of Riemann's Theorem: Let (A,\Theta) be an indecomposable principally polarized abelian variety whose theta divisor can be written as a sum of a curve and a codimension two subvariety \Theta=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 solve the DPC Problem for theta divisors and characterize Jacobians by the existence of a d-dimensional subvariety with curve summand whose twisted ideal sheaf is a GV-sheaf.

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