Maps of
complex hyperbolic surfaces
Abstract
We
study a class of examples of surjective holomorphic maps between compact
two-dimensional ball quotients that are not covering maps. We find all
such maps that can be written in terms of hypergeometric functions.
They have the property that the induced homomorphism in fundamental groups is
not injective. They include Mostow's example of a non-injective
homomorphism, and are motivated by that example. We study the
singularity behavior of these maps, and state a number of natural problems
that are suggested by these examples.
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