Summands of theta divisors on Jacobians

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jul 2020Embargo end date: 27 Nov 2023 Germany English Publisher:Cambridge University Press (CUP)Journal:Compositio Mathematica, volume 156, pages 1,457-1,475 (issn: 0010-437X, eissn: 1570-5846,

Copyright policy )

Authors: Krämer, Thomas;

doi: 10.1112/s0010437x20007204 , 10.18452/27787 , 10.48550/arxiv.1811.01072

arXiv: 1811.01072

Summands of theta divisors on Jacobians

- Summary
- Subjects
- Metrics

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.

Country

Germany

Related Organizations

Humboldt-Universität zu Berlin
Germany

Keywords

Representation theory for linear algebraic groups, 14K12, 14F10, 18D10, 20G05, Subvarieties of abelian varieties, Mathematics - Algebraic Geometry, characteristic cycle, Tannakian category, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, FOS: Mathematics, perverse sheaf, 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, theta divisor, Tannakian categories, Representation Theory (math.RT), Algebraic Geometry (math.AG), ddc:510, 510 Mathematik, Jacobian variety, Gauss map, 14K12: Subvarieties, 18D10: Monoidal categories (= multiplicative categories), symmetric monoidal categories, braided categories, Mathematics - Representation Theory

Impact byBIP!

	selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	2
	popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.	Average
	influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).	Average
	impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.	Average