Counting rational maps onto surfaces and fundamental groups

T. Bandman; A. Libgober

doi:10.1142/S0129167X04002508

Counting rational maps onto surfaces and fundamental groups

T. Bandman, A. Libgober

Department of Mathematics

University of Illinois at Chicago

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	673-690
Number of pages	18
Journal	International Journal of Mathematics
Volume	15
Issue number	7
DOIs	https://doi.org/10.1142/S0129167X04002508
State	Published - Sep 2004

Bibliographical note

Funding Information:
The first author is supported by the Ministry of Absorption (Israel), the Israeli Science Foundation (Israeli Academy of Sciences, Center of Excellence Program), the Minerva Foundation (Emmy Noether Research Institute of Mathematics). The second author is supported by NSF grant.

Funding

The first author is supported by the Ministry of Absorption (Israel), the Israeli Science Foundation (Israeli Academy of Sciences, Center of Excellence Program), the Minerva Foundation (Emmy Noether Research Institute of Mathematics). The second author is supported by NSF grant.

Funders	Funder number
Israeli Academy of Sciences
Ministry of Absorption
National Science Foundation
Minerva Foundation
Israel Science Foundation

Keywords

Affine varieties
Characteristic variety of fundamental group
Fundamental group
Local systems
Rational maps

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10.1142/S0129167X04002508

Cite this

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author = "T. Bandman and A. Libgober",

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KW - Characteristic variety of fundamental group

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KW - Local systems

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Counting rational maps onto surfaces and fundamental groups

Abstract

Bibliographical note

Funding

Keywords

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