Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0404062,
title = {Moduli Space of Cubic Surfaces as Ball Quotient via Hypergeometric Functions},
author = {Brent R. Doran},
journal= {arXiv preprint arXiv:math/0404062},
year = {2007}
}