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

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

2007-10-29

arxiv.org/abs/0710.5329v2

J. Reine Angew. Math. 633 (2009), 29-65

Mathematics

Algebraic Geometry

35 pages, final version

Scientific paper

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.

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