Counting rational maps onto surfaces and fundamental groups

Details Counting rational maps onto surfaces and fundamental groups Counting rational maps onto surfaces and fundamental groups

2004-05-02

arxiv.org/abs/math/0405018v1

Mathematics

Algebraic Geometry

19 pages, AMSTeX

Scientific paper

We consider the class of quasiprojective varieties admitting a dominant morphism onto a curve with negative Euler characteristic. The existence of such a morphism is a property of the fundamental group. We show that for a variety in this class the number of maps onto a hyperbolic curve or surfaces can be estimated in terms of the numerical invariants of the fundamental group. We use this estimates to find the number of biholomorphic automorphisms of complements to some arrangements of lines.

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