Inverse degree of an affine space triangular automorphism

Author:
Shu Kawaguchi

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3353-3360

MSC (2010):
Primary 08A35, 13B25, 14J50, 14R10

DOI:
https://doi.org/10.1090/S0002-9939-2013-11631-X

Published electronically:
June 17, 2013

MathSciNet review:
3080158

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Abstract | References | Similar Articles | Additional Information

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 Abhyankar-Gurjar'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 560-0043, Japan

Address at time of publication:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan

Email:
kawaguch@math.sci.osaka-u.ac.jp, kawaguch@math.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-2013-11631-X

Keywords:
Automorphism,
degree,
inverse,
polynomial ring,
non-reduced 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.