English

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.

Keywords

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}
}
R2 v1 2026-06-22T01:20:25.325Z