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Finite subschemes of abelian varieties and the Schottky problem

Martin G. GulbrandsenMartí Lahoz — 2011

Annales de l’institut Fourier

The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties ( A , Θ ) of dimension g , by the existence of g + 2 points Γ A in special position with respect to 2 Θ , but general with respect to Θ , 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...

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