The moduli space of cubic threefolds via degenerations of the intermediate Jacobian

A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of these abelian varieties, and thus give a description of the compactification of the moduli space of cubic threefolds...

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Bibliographic Details
Published in:Journal für die reine und angewandte Mathematik 2009-08, Vol.2009 (633), p.29-65
Main Authors: Casalaina-Martin, Sebastian, Laza, Radu
Format: Article
Language:English
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Summary:A well known result of Clemens and Griffiths says that a smooth cubic threefold can be recovered from its intermediate Jacobian. In this paper we discuss the possible degenerations of these abelian varieties, and thus give a description of the compactification of the moduli space of cubic threefolds obtained in this way. The relation between this compactification and those constructed in the work of Allcock-Carlson-Toledo and Looijenga-Swierstra is also considered, and is similar in spirit to the relation between the various compactifications of the moduli spaces of low genus curves.
ISSN:0075-4102
1435-5345
DOI:10.1515/CRELLE.2009.059