# name
Finite subschemes of abelian varieties and the Schottky problem

# metadata.dc.description.abstract[].value
The Castelnuovo-Schottky theorem of Pareschi-Popa characterizes Jacobians, among indecomposable principally polarized abelian varieties $(A,\Theta)$ of dimension $g$, by the existence of $g+2$ points $\Gamma \subset A$ in special position with respect to $2 \Theta$, but general with respect to $\Theta$, 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 $\Gamma$.

# metadata.dc.publisher[].value
Association des Annales de l'Institut Fourier

# metadata.dc.rights[].value
(c) Association des Annales de l'Institut Fourier, 2011

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Finite subschemes of abelian varieties and the Schottky problem