Affine smooth varieties with finite group of automorphisms
type: Item
instance of: scholarly article
title: Affine smooth varieties with finite group of automorphisms
zbMATH Open document ID: 0824.14012
DOI: 10.1007/BF02572340
author: Z. Jelonek
published in: Mathematische Zeitschrift
publication date: 1995-11-16T00:00:00Z
full work available at URL: https://eudml.org/doc/174669
review text: The paper concerns automorphism groups of Zariski open subsets of smooth projective varieties \(X\) over \(\mathbb{C}\). The main problems, considered in the paper, are: 1. under what conditions for a divisor \(H \subset X\) the group of automorphisms \(\Aut (X \backslash H)\) is finite; 2. when an automorphism of \(X \backslash H\) can be extended to an automorphism of \(X\); 3. for which subgroup \(G\) of \(\Aut (X)\) does there exist a divisor \(H \subset X\) such that \(\Aut (X \backslash H) = G\). The main answers, given in the paper, to these questions are: Ad 1. \(H\) does not have uniruled components and is a very ample divisor; Ad 2. the same as above; Ad 3. \(G\) finite. There is also many applications of these results to particular cases.
Mathematics Subject Classification ID: 14H37
Mathematics Subject Classification ID: 14E07
zbMATH DE Number: 703847
zbMATH Keywords: finiteness of automorphism group
zbMATH Keywords: extension of automorphism group
zbMATH Keywords: hypersurface
zbMATH Keywords: divisor
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 703847