Finite subschemes of abelian varieties and the Schottky problem

Details Finite subschemes of abelian varieties and the Schottky problem Finite subschemes of abelian varieties and the Schottky problem

2010-04-09

arxiv.org/abs/1004.1495v2

Ann Inst. Fourier 61 (2011), no. 5, 2039-2064

Mathematics

Algebraic Geometry

22 pages. A few expository changes and some references added according to suggestions from the referee. To appear in Annales d

Scientific paper

The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties of dimension g, by the existence of g+2 points in general position with respect to the principal polarization, but special with respect to twice the polarization, and furthermore states that such collections of points must be contained in an Abel-Jacobi curve. Building on the ideas in the original paper, we give here a self contained, scheme theoretic proof of the theorem, extending it to finite, possibly nonreduced subschemes.

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