We define hypergeometric functions using intersection homology valued in alocal system. Topology is emphasized; analysis enters only once, via the Hodgedecomposition. By a pull-back procedure we construct special subsets S_{pi},derived from Hurwitz spaces, of Deligne-Mostow moduli spaces DM(n,mu). CertainDM(n,mu) are known to be ball quotients, uniformized by hypergeometricfunctions valued in a complex ball (i.e., complex hyperbolic space). We givesufficient conditions for S_{pi} to be a subball quotient. Analyzing thesimplest examples in detail, we describe ball quotient structures attached tosome moduli spaces of inhomogeneous binary forms. This recovers in particularthe structure on the moduli space of rational elliptic surfaces given byHeckman and Looijenga. We make use of a natural partial ordering on theDeligne-Mostow examples (which gives an easy way to see that the original listof Mostow, eventually corrected by Thurston, is in error), and so highlight twokey examples, which we call the Gaussian and Eisenstein ancestral examples.
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