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A new geometric proof of Jung's theorem on factorisation of automorphisms of $\mathbb{C} ^2$


Author: Javier Fernández de Bobadilla
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
Published electronically: July 22, 2004
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Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. H.W.E. Jung. Über ganze birationale Transformationen der Ebene., J. Reine Angew. Math. 184 (1942), 161-174. MR 0008915 (5:74f)
  • 2. M. Nagata, On automorphism group of $k[x,y]$, Lectures in Mathematics, Department of Mathematics, Kyoto University, 5 (1972). MR 0337962 (49:2731)
  • 3. H. Yoshihara. Projective plane curves and the automorphism groups of their complements, J. Math. Soc. Japan 37 no.1 (1985), 87-113. MR 0769779 (87f:14015)

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Additional Information

Javier Fernández de Bobadilla
Affiliation: Mathematisch Instituut, Universiteit Utrecht, Postbus 80010, 3508TA Utrecht, The Netherlands
Email: bobadilla@math.uu.nl

DOI: https://doi.org/10.1090/S0002-9939-04-07637-3
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
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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