Summands of theta divisors on Jacobians

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...

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Bibliographic Details
Published inCompositio mathematica Vol. 156; no. 7; pp. 1457 - 1475
Main Author Krämer, Thomas
Format Journal Article
LanguageEnglish
Published London, UK London Mathematical Society 01.07.2020
Cambridge University Press
Subjects
Decomposition
Jacobians
Sheaves
18D10
Jacobian variety
Gauss map
14K12
perverse sheaf
theta divisor
14F10
20G05
characteristic cycle
Tannakian category
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X20007204