Local construction of complex algebraic surfaces with respect to the universal covering
type: Item
instance of: scholarly article
title: Local construction of complex algebraic surfaces with respect to the universal covering
zbMATH Open document ID: 0543.14007
DOI: 10.1007/BF01083150
author: N. E. Zubov
publication date: 1983-01-01T00:00:00Z
review text: The author studies a morphism \(\pi: X\to S\) from a smooth complex algebraic surface to a smooth complex curve which is locally trivial from the differential viewpoint. He assumes that the fundamental groups of the base and the fibre are non-commutative, and that the universal covering \(\tilde X\) is not a bidisk. He indicates the proofs for the following results: The group \(\Aut \tilde X\) of all biholomorphic automorphisms is countable. The fundamental group \(\pi_1(X)\) has finite index in \(\Aut \tilde X\). There are only finitely many subgroups of \(\Aut \tilde X\) which act properly discontinuously and are isomorphic to \(\pi_1(X)\).
reviewed by: Klaus Lamotke
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 32M05
Mathematics Subject Classification ID: 32J25
Mathematics Subject Classification ID: 14M07
Mathematics Subject Classification ID: 14L30
Mathematics Subject Classification ID: 14F35
zbMATH DE Number: 3863345
zbMATH Keywords: hyperbolic curve
zbMATH Keywords: group of biholomorphic automorphisms
zbMATH Keywords: fundamental group
MaRDI profile type: Publication
cites work: Q4760224
cites work: Complex-analytic properties of certain Zariski open sets on algebraic varieties
cites work: Strong rigidity of Q-rank 1 lattices
full work available at URL: https://doi.org/10.1007/bf01083150
OpenAlex ID: W1976923770
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published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 3863345