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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Arithmetic Torelli maps for cubic surfaces and threefolds


Author: Jeffrey D. Achter
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14J10; Secondary 11G18, 14H40, 14K30
Published electronically: June 16, 2014
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Abstract: It has long been known that to a complex cubic surface or threefold one can canonically associate a principally polarized abelian variety. We give a construction which works for cubics over an arithmetic base, and in particular identifies the moduli space of cubic surfaces with an open substack of a certain moduli space of abelian varieties. This answers, away from the prime $ 2$, an old question of Deligne and a recent question of Kudla and Rapoport.


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Additional Information

Jeffrey D. Achter
Affiliation: Department of Mathematics, Colorado State University, Fort Collins, Colorado 80523
Email: j.achter@colostate.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-05978-3
PII: S 0002-9947(2014)05978-3
Received by editor(s): February 16, 2012
Received by editor(s) in revised form: September 11, 2012
Published electronically: June 16, 2014
Additional Notes: This work was partially supported by a grant from the Simons Foundation (204164).
Article copyright: © Copyright 2014 American Mathematical Society