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A Special Case of the Γ00 Conjecture

  • Samuel Grushevsky
Part of the Progress in Mathematics book series (PM, volume 280)

Abstract

In this paper we prove the Γ00 conjecture of van Geemen and van der Geer [8] under the additional assumption that the matrix of coefficients of the tangent has rank at most 2 (see Theorem 1 for a precise formulation). This assumption is satisfied by Jacobians (see proposition 1), and thus our result gives a characterization of the locus of Jacobians among all principally polarized abelian varieties.

The proof is by reduction to the (stronger version of the) characterization of Jacobians by semidegenerate trisecants, i.e., by the existence of lines tangent to the Kummer variety at one point and intersecting it in another, proven by Krichever in [16] in his proof of Welters’ [20] trisecant conjecture.

Mathematics Subject Classification (2000)

14H42 14H40 32G15 

Keywords

Jacobian abelian variety theta function Schottky problem 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2010

Authors and Affiliations

  • Samuel Grushevsky
    • 1
  1. 1.Mathematics DepartmentPrinceton UniversityPrincetonUSA

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