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Cubic threefolds and abelian varieties of dimension five

Sebastian Casalaina-Martin·Robert Friedman
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Abstract

This paper proves the following converse to a theorem of Mumford: Let $A$ be a principally polarized abelian variety of dimension five, whose theta divisor has a unique singular point, and suppose that the multiplicity of the singular point is three. Then $A$ is isomorphic as a principally polarized abelian variety to the intermediate Jacobian of a smooth cubic threefold. The method of proof is to analyze the possible singularities of the theta divisor of $A$, and eventually to show that $A$ is the Prym variety of a possibly singular plane quintic.

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BibTeXRIS

Sebastian Casalaina-Martin, Robert Friedman. 2003-07-28. Cubic threefolds and abelian varieties of dimension five. https://arxiv.org/abs/math/0307015

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