Arithmetic Torelli maps for cubic surfaces and threefolds
Algebraic Geometry
2020-02-27 v4
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. 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.
Cite
@article{arxiv.1005.2131,
title = {Arithmetic Torelli maps for cubic surfaces and threefolds},
author = {Jeff Achter},
journal= {arXiv preprint arXiv:1005.2131},
year = {2020}
}