A Picard modular fourfold and the Weyl group W(E_6)
Bert van Geemen, Kenji Koike
TL;DR
This paper investigates the geometry of a specific Picard modular fourfold related to abelian fourfolds of Weil type, providing a projective model, describing the Weyl group action, and analyzing special subvarieties and boundaries.
Contribution
It offers a new explicit projective model of the Picard modular fourfold and details the Weyl group W(E_6) action on it, along with geometric substructures.
Findings
Explicit projective model as a degree ten hypersurface in P^5
Description of Weyl group W(E_6) action on the fourfold
Identification of special subvarieties and boundary components
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Finite Group Theory Research