Counting rational maps onto surfaces and fundamental groups

2004/05/02 by Tatiana Bandman, T. Bandman, Bandman, T. +3
Computer Science · Mathematics · Physics and Astronomy · #14FXX #14R25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.AG #msc:14FXX #msc:14R25

paper · pdf · doi:10.48550/arxiv.math/0405018

19 pages, AMSTeX

arxiv created 2004/05/02 · openalex publication_date 2004/05/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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