Counting rational maps onto surfaces and fundamental groups
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0405018,
title = {Counting rational maps onto surfaces and fundamental groups},
author = {T. Bandman and A. Libgober},
journal= {arXiv preprint arXiv:math/0405018},
year = {2007}
}
Comments
19 pages, AMSTeX