The automorphism groups of Zariski open affine subsets of the affine plane

Zbigniew Jelonek

Annales Polonici Mathematici (1994)

  • Volume: 60, Issue: 2, page 163-171
  • ISSN: 0066-2216

Abstract

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We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.

How to cite

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Zbigniew Jelonek. "The automorphism groups of Zariski open affine subsets of the affine plane." Annales Polonici Mathematici 60.2 (1994): 163-171. <http://eudml.org/doc/262297>.

@article{ZbigniewJelonek1994,
abstract = {We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.},
author = {Zbigniew Jelonek},
journal = {Annales Polonici Mathematici},
keywords = {polynomial automorphisms; the set of fixed points of a polynomial automorphism; the affine plane; affine plane; polynomial automorphism; fixed points},
language = {eng},
number = {2},
pages = {163-171},
title = {The automorphism groups of Zariski open affine subsets of the affine plane},
url = {http://eudml.org/doc/262297},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Zbigniew Jelonek
TI - The automorphism groups of Zariski open affine subsets of the affine plane
JO - Annales Polonici Mathematici
PY - 1994
VL - 60
IS - 2
SP - 163
EP - 171
AB - We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.
LA - eng
KW - polynomial automorphisms; the set of fixed points of a polynomial automorphism; the affine plane; affine plane; polynomial automorphism; fixed points
UR - http://eudml.org/doc/262297
ER -

References

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  14. [Suz1] M. Suzuki, Propriétés topologiques des polynômes de deux variables complexes, et automorphismes algébriques de l'espace ℂ², J. Math. Soc. Japan 26 (1974), 241-257. Zbl0276.14001
  15. [Suz2] M. Suzuki, Sur les opérations holomorphes du groupe additif complexe sur l'espace de deux variables complexes, Ann. Sci. Ecole Norm. Sup. 10 (1977), 517-546. Zbl0403.32020
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