English

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.

Keywords

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

R2 v1 2026-06-21T21:50:40.782Z