A special case of the $Γ_{00}$ conjecture

Details A special case of the $Γ_{00}$ conjecture A special case of the $Γ_{00}$ conjecture

2008-04-03

arxiv.org/abs/0804.0525v3

Mathematics

Algebraic Geometry

v2: References updated and corrected; v3: final version, stronger result statement (rank at most 2 instead or rank 1)

Scientific paper

In this paper we prove the $\Gamma_{00}$ conjecture of van Geemen and van der Geer, under the additional assumption that the matrix of coefficients of the tangent has rank at most 2. This assumption is satisfied by Jacobians, 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 the course of his proof of the Welters' trisecant conjecture.

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