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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

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

Sebastian Casalaina-Martin1 / Radu Laza2

1Department of Mathematics, Harvard University, Cambridge, MA 02138, USA. e-mail:

2Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA. e-mail:

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal). Volume 2009, Issue 633, Pages 29–65, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/CRELLE.2009.059, June 2009

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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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