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2011

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/124869

Finite subschemes of abelian varieties and the Schottky problem

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https://doi.org/10.5802/aif.2665

Abstract

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 $\Gamma$.

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Corbes, Varietats abelianes

Subject (English)

Curves, Abelian varieties

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

GULBRANDSEN, Martin G. and LAHOZ VILALTA, Martí. Finite subschemes of abelian varieties and the Schottky problem. Annales de l'Institut Fourier. 2011. Vol. 61, num. 5, pags. 2039-2064. ISSN 0373-0956. [consulted: 17 of August of 2026]. Available at: https://hdl.handle.net/2445/124869

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