A Picard modular fourfold and the Weyl group W(E_6)
Algebraic Geometry
2013-09-05 v1
Abstract
We study the geometry of a Picard modular fourfold which parametrizes abelian fourfolds of Weil type for the field of cube roots of unity. We find a projective model of this fourfold as a singular, degree ten, hypersurface X in projective 5-space. The Weyl group W(E_6) acts on X and we provide an explicit description of this action. Moreover, we describe various special subvarieties as well as the boundary of X.
Cite
@article{arxiv.1309.0963,
title = {A Picard modular fourfold and the Weyl group W(E_6)},
author = {Bert van Geemen and Kenji Koike},
journal= {arXiv preprint arXiv:1309.0963},
year = {2013}
}