Theta divisors with curve summands and the Schottky problem

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Stefan Schreieder

External Research Organisations

  • Max Planck Institute for Mathematics
  • University of Bonn
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Details

Original languageEnglish
Pages (from-to)1017-1039
Number of pages23
JournalMathematische Annalen
Volume365
Issue number3-4
Publication statusPublished - 1 Aug 2016
Externally publishedYes

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 Wg - 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.

Keywords

    Schottky Problem, DPC Problem, Theta divisors, Jacobians, generic vanishing

ASJC Scopus subject areas

Cite this

Theta divisors with curve summands and the Schottky problem. / Schreieder, Stefan.
In: Mathematische Annalen, Vol. 365, No. 3-4, 01.08.2016, p. 1017-1039.

Research output: Contribution to journal › Article › Research › peer review

Schreieder S. Theta divisors with curve summands and the Schottky problem. Mathematische Annalen. 2016 Aug 1;365(3-4):1017-1039. doi: 10.1007/s00208-015-1287-8
Schreieder, Stefan. / Theta divisors with curve summands and the Schottky problem. In: Mathematische Annalen. 2016 ; Vol. 365, No. 3-4. pp. 1017-1039.
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