Arithmetic Torelli maps for cubic surfaces and threefolds

Achter, Jeffrey

doi:10.1090/S0002-9947-2014-05978-3

Arithmetic Torelli maps for cubic surfaces and threefolds
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by Jeffrey D. Achter PDF

Trans. Amer. Math. Soc. 366 (2014), 5749-5769 Request permission

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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