A new geometric proof of Jung’s theorem on factorisation of automorphisms of $\mathbb {C}^2$
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- by Javier Fernández de Bobadilla
- Proc. Amer. Math. Soc. 133 (2005), 15-19
- DOI: https://doi.org/10.1090/S0002-9939-04-07637-3
- Published electronically: July 22, 2004
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Abstract:
Building up on the classical theory of algebraic surfaces and their birational transformations we prove Jung’s theorem on factorisation of automorphisms of $\mathbb {C}^2$ reducing it to a simple combinatorial argument.References
- Heinrich W. E. Jung, Über ganze birationale Transformationen der Ebene, J. Reine Angew. Math. 184 (1942), 161–174 (German). MR 8915, DOI 10.1515/crll.1942.184.161
- Masayoshi Nagata, On automorphism group of $k[x,\,y]$, Kinokuniya Book Store Co., Ltd., Tokyo, 1972. Department of Mathematics, Kyoto University, Lectures in Mathematics, No. 5. MR 0337962
- Hisao Yoshihara, Projective plane curves and the automorphism groups of their complements, J. Math. Soc. Japan 37 (1985), no. 1, 87–113. MR 769779, DOI 10.2969/jmsj/03710087
Bibliographic Information
- Javier Fernández de Bobadilla
- Affiliation: Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508TA Utrecht, The Netherlands
- Email: bobadilla@math.uu.nl
- Received by editor(s): June 5, 2002
- Received by editor(s) in revised form: September 6, 2003
- Published electronically: July 22, 2004
- Additional Notes: This work was supported by a fellowship of the Banco de España
- Communicated by: Michael Stillman
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 15-19
- MSC (2000): Primary 14E07, 14R10, 13M10
- DOI: https://doi.org/10.1090/S0002-9939-04-07637-3
- MathSciNet review: 2085147