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1994-1995 | 60 | 2 | 163-171
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Tom
60
Numer
2
Strony
163-171
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-10-21
poprawiono
1994-02-10
Twórcy
  • Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
Bibliografia
  • [A-M] S. Abhyankar and T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148-166.
  • [Iit1] S. Iitaka, On logarithmic Kodaira dimension of algebraic varieties, in: Complex Analysis and Algebraic Geometry, Iwanami, Tokyo, 1977, 178-189.
  • [Iit2] S. Iitaka, Birational Geometry for Open Varieties, Les Presses de L'Université de Montréal, 1981.
  • [Jel1] Z. Jelonek, Identity sets for polynomial automorphisms, J. Pure Appl. Algebra 76 (1991), 333-339.
  • [Jel2] Z. Jelonek, Irreducible identity sets for polynomial automorphisms, Math. Z. 212 (1993), 601-617.
  • [Jel3] Z. Jelonek, Affine smooth varieties with finite group of automorphisms, ibid., to appear.
  • [Jel4] Z. Jelonek, The extension of regular and rational embeddings, Math. Ann. 277 (1987), 113-120.
  • [Jel5] Z. Jelonek, Sets determining polynomial automorphisms of ℂ², Bull. Polish Acad. Sci. Math. 37 (1989), 247-250.
  • [Kal] S. Kaliman, Polynomials on ℂ² with isomorphic generic fibers, Soviet Math. Dokl. 33 (1986), 600-603.
  • [Kam] T. Kambayashi, Automorphism group of a polynomial ring and algebraic group action on an affine space, J. Algebra 60 (1979), 439-451.
  • [Kul] W. van der Kulk, On polynomial rings in two variables, Nieuw Arch. Wisk. 1 (1953), 33-41.
  • [M-W] J. MacKay and S. Wang, An inversion formula for two polynomials in two variables, J. Pure Appl. Algebra 76 (1986), 245-257.
  • [Sak] F. Sakai, Kodaira dimension of complements of divisors, in: Complex Analysis and Algebraic Geometry, Iwanami, Tokyo, 1977, 239-257.
  • [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.
  • [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.
  • [Zai] M. G. Zaĭdenberg, Isotrivial families of curves on affine surfaces and characterization of the affine plane, Math. USSR-Izv. 30 (1988), 503-532.
  • [Z-L] M. G. Zaĭdenberg and V. Ya. Lin, An irreducible simply connected algebraic curve in ℂ² is equivalent to a quasihomogeneous curve, Soviet Math. Dokl. 28 (1983), 200-203.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv60z2p163bwm
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