Decomposable theta divisors and generic vanishing

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Stefan Schreieder

Externe Organisationen

  • Rheinische Friedrich-Wilhelms-Universität Bonn
Forschungs-netzwerk anzeigen

Details

OriginalspracheEnglisch
Seiten (von - bis) 4984-5009
Seitenumfang26
FachzeitschriftInternational Mathematics Research Notices
Jahrgang2017
Ausgabenummer16
PublikationsstatusVeröffentlicht - 2017
Extern publiziertJa

Abstract

We study ample divisors X with only rational singularities on abelian varieties that decompose into a sum of two lower dimensional subvarieties, X = V + W . For instance, we prove an optimal lower bound on the degree of the addition map V × W X and show that the minimum can only be achieved if X is a theta divisor. Conjecturally, the latter happens only on Jacobians of curves and intermediate Jacobians of cubic threefolds. As an application, we prove that nondegenerate generic vanishing subschemes of indecomposable principally polarized abelian varieties are automatically reduced and irreducible, have the expected geometric genus, and property (P) with respect to their theta duals.

ASJC Scopus Sachgebiete

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Decomposable theta divisors and generic vanishing. / Schreieder, Stefan.
in: International Mathematics Research Notices, Jahrgang 2017, Nr. 16, 2017, S. 4984-5009.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Schreieder S. Decomposable theta divisors and generic vanishing. International Mathematics Research Notices. 2017;2017(16): 4984-5009. doi: 10.1093/imrn/rnw160
Schreieder, Stefan. / Decomposable theta divisors and generic vanishing. in: International Mathematics Research Notices. 2017 ; Jahrgang 2017, Nr. 16. S. 4984-5009.
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