Birational morphisms of the plane
Authors:
Vladimir Shpilrain and JieTai Yu
Journal:
Proc. Amer. Math. Soc. 132 (2004), 25112515
MSC (2000):
Primary 14E07, 14E25; Secondary 14A10, 13B25
Published electronically:
April 8, 2004
MathSciNet review:
2054774
Fulltext PDF Free Access
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Abstract: Let be the affine plane over a field of characteristic . Birational morphisms of are mappings given by polynomial mappings of the polynomial algebra such that for the quotient fields, one has . Polynomial automorphisms are obvious examples of such mappings. Another obvious example is the mapping given by . For a while, it was an open question whether every birational morphism is a product of polynomial automorphisms and copies of . This question was answered in the negative by P. Russell (in an informal communication). In this paper, we give a simple combinatorial solution of the same problem. More importantly, our method yields an algorithm for deciding whether a given birational morphism can be factored that way.
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Additional Information
Vladimir Shpilrain
Affiliation:
Department of Mathematics, The City College of New York, New York, New York 10031
Email:
shpil@groups.sci.ccny.cuny.edu
JieTai Yu
Affiliation:
Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong
Email:
yujt@hkusua.hku.hk
DOI:
http://dx.doi.org/10.1090/S0002993904074908
PII:
S 00029939(04)074908
Keywords:
Affine plane,
birational morphisms,
peak reduction
Received by editor(s):
November 13, 2002
Published electronically:
April 8, 2004
Additional Notes:
The second author was partially supported by RGC Grant Project 7126/98P
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2004
American Mathematical Society
