Arithmetic Torelli maps for cubic surfaces and threefolds

Details Arithmetic Torelli maps for cubic surfaces and threefolds Arithmetic Torelli maps for cubic surfaces and threefolds

2010-05-12

arxiv.org/abs/1005.2131v3

Mathematics

Algebraic Geometry

More information on Prym construction

Scientific paper

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. This answers, away from the prime 2, an old question of Deligne and a recent question of Kudla and Rapoport. We further classify the Mumford-Tate groups of the abelian varieties which arise, and give additional arithmetic applications.

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