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