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(E6) 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.
A Picard modular fourfold and the Weyl group W(E6) / L. van Geemen, K. Koike. - In: COMMUNICATIONS IN ANALYSIS AND GEOMETRY. - ISSN 1019-8385. - 23:5(2015), pp. 923-949. [10.4310/CAG.2015.v23.n5.a1]
A Picard modular fourfold and the Weyl group W(E6)
L. van GeemenPrimo
;
2015
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(E6) 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.
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