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Summands of theta divisors on Jacobians

Part of: Abelian varieties and schemes (Co)homology theory Linear algebraic groups and related topics Categories with structure

Published online by Cambridge University Press:  08 July 2020

Thomas Krämer
Thomas Krämer*
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099Berlin, Germany email thomas.kraemer@math.hu-berlin.de
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Abstract

We show that the only summands of the theta divisor on Jacobians of curves and on intermediate Jacobians of cubic threefolds are the powers of the curve and the Fano surface of lines on the threefold. The proof only uses the decomposition theorem for perverse sheaves, some representation theory and the notion of characteristic cycles.

Keywords

Jacobian varietytheta divisorGauss mapcharacteristic cycleperverse sheafTannakian category

MSC classification

Primary: 14K12: Subvarieties
Secondary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories 20G05: Representation theory
Type
Research Article
Information
Compositio Mathematica , Volume 156 , Issue 7 , July 2020 , pp. 1457 - 1475
Copyright
© The Author 2020

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