On the abelian fivefolds attached to cubic surfaces
Algebraic Geometry
2020-02-27 v2 Number Theory
Abstract
To a family of smooth projective cubic surfaces one can canonically associate a family of abelian fivefolds. In characteristic zero, we calculate the Hodge groups of the abelian varieties which arise in this way. In arbitrary characteristic we calculate the monodromy group of the universal family of abelian varieties, and thus show that the Galois group of the 27 lines on a suitably general cubic surface in positive characteristic is as large as possible.
Cite
@article{arxiv.1208.2974,
title = {On the abelian fivefolds attached to cubic surfaces},
author = {Jeff Achter},
journal= {arXiv preprint arXiv:1208.2974},
year = {2020}
}
Comments
Fixed classification of Hodge groups; other small edits