On a family of surfaces of general type attached to abelian fourfolds and the Weyl group W(E_6)

Abstract

We study a family of surfaces of general type that arises from the intersections of two translates of the theta divisor on a principally polarized complex abelian fourfold. In particular we determine the Néron-Severi lattices of these surfaces and show that for a general abelian fourfold the monodromy group of the associated variation of Hodge structures is a subgroup of index at most two in the Weyl group W(E_6), whereas for a Jacobian variety it degenerates to a subgroup of the symmetric group S_6.

29 pages

References in corpus (5)

• Vanishing Theorems for constructible Sheaves on Abelian Varieties
• Brill-Noether Sheaves
• On the Tannaka group attached to the Theta divisor of a generic principally polarized abelian variety
• A Remark on Rigidity of BN-sheaves
• Tannakian Categories attached to abelian Varieties

Cited by in corpus (2)

• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• Characteristic classes and Hilbert-Poincaré series for perverse sheaves on abelian varieties