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A well known result of Clemens and Griffiths says that a smooth cubicthreefold can be recovered from its intermediate Jacobian. In this paper wediscuss the possible degenerations of these abelian varieties, and thus give adescription of the compactification of the moduli space of cubic threefoldsobtained in this way. The relation between this compactification and thoseconstructed in the work of Allcock-Carlson-Toledo and Looijenga-Swierstra isalso considered, and is similar in spirit to the relation between the variouscompactifications of the moduli spaces of low genus curves.

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