Irreducible identity sets for polynomial automorphisms
type: Item
instance of: scholarly article
title: Irreducible identity sets for polynomial automorphisms
zbMATH Open document ID: 0806.14011
DOI: 10.1007/BF02571679
author: Z. Jelonek
published in: Mathematische Zeitschrift
publication date: 1995-02-19T00:00:00Z
full work available at URL: https://eudml.org/doc/174508
review text: The author studies polynomial automorphisms of algebraic, affine and projective, varieties over \(\mathbb{C}\). First, he proves that every \((n-1)\)- dimensional component of the set of fixed points of a polynomial automorphism of \(\mathbb{C}^ n\) is uniruled at infinity. Second, he gives classes of hypersurfaces which are identity sets for polynomial automorphisms and sets determining polynomial automorphisms of \(\mathbb{C}^ n\), respectively. Third, he gives classes of hypersurfaces \(V\) in projective manifolds \(X\) (in particular in \(\mathbb{P}^ n (\mathbb{C})\) and \(\mathbb{C}^ n)\) for which every polynomial automorphism of the set \(X \backslash V\) can be extended to a polynomial automorphism of \(X\).
Mathematics Subject Classification ID: 14J50
Mathematics Subject Classification ID: 32H25
Mathematics Subject Classification ID: 14J26
Mathematics Subject Classification ID: 13F20
zbMATH DE Number: 549754
zbMATH Keywords: uniruled variety
zbMATH Keywords: polynomial automorphisms
zbMATH Keywords: identity sets
reviewed by: Tadeusz Krasiński
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 549754