Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions

Details Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions

2004-04-04

arxiv.org/abs/math/0404062v1

Mathematics

Algebraic Geometry

Scientific paper

We describe hypergeometric functions of Deligne-Mostow type for open subsets of the configuration space of six points on P^2, induced from those for seven points on P^1. The seven point ball quotient example DM(2^5,1^2) does not appear on Mostow's original list, but does appear on Thurston's corrected version. We show that DM(2^5,1^2) is a finite cover of the moduli space of cubic surfaces M_C endowed with the ball quotient structure G_C\B^4 of Allcock, Carlson, and Toledo. This answers a question of Allcock about the commensurability of G_C with the monodromy groups of Deligne-Mostow hypergeometric functions.

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