Inverse degree of an affine space triangular automorphism
Author:
Shu Kawaguchi
Journal:
Proc. Amer. Math. Soc. 141 (2013), 33533360
MSC (2010):
Primary 08A35, 13B25, 14J50, 14R10
Published electronically:
June 17, 2013
MathSciNet review:
3080158
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Abstract: For any algebra and any triangular automorphism with Jacobian one on the affine space, we show that is bounded from above by a constant depending only on and . This is seen as a generalization of a result by Furter on the affine plane. Our proof uses (a version of) Furter's estimate on nilpotency indices and AbhyankarGurjar's formal inversion formula. It follows that when the Jacobian of a triangular automorphism is not necessarily equal to one, is bounded from above by a constant depending only on , and .
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Additional Information
Shu Kawaguchi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 5600043, Japan
Address at time of publication:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 6068502, Japan
Email:
kawaguch@math.sci.osakau.ac.jp, kawaguch@math.kyotou.ac.jp
DOI:
http://dx.doi.org/10.1090/S00029939201311631X
Keywords:
Automorphism,
degree,
inverse,
polynomial ring,
nonreduced ring
Received by editor(s):
October 18, 2010
Received by editor(s) in revised form:
December 13, 2011
Published electronically:
June 17, 2013
Additional Notes:
This work is partially supported by KAKENHI 21740018
Communicated by:
Harm Derksen
Article copyright:
© Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
