Degree bounds for inverses of polynomial automorphisms
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- by Charles Ching-an Cheng, Stuart Sui Sheng Wang and Jie Tai Yu PDF
- Proc. Amer. Math. Soc. 120 (1994), 705-707 Request permission
Abstract:
It is known that if $k$ is a field and ${\mathbf {F}}:k[{X_1}, \ldots ,{X_n}] \to k[{X_1}, \ldots ,{X_n}]$ is a polynomial automorphism, then $\deg ({{\mathbf {F}}^{ - 1}}) \leqslant {(\deg {\mathbf {F}})^{n - 1}}$. We extend this result to the case where $k$ is a reduced ring. Furthermore, if $k$ is not a reduced ring, we show that for any integer $n \geqslant 1$ and any integer $\lambda \geqslant 0$ there exists a polynomial automorphism ${\mathbf {F}}$ such that $\deg ({{\mathbf {F}}^{ - 1}}) = \lambda + {(\deg {\mathbf {F}})^{n - 1}}$.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 705-707
- MSC: Primary 14E07
- DOI: https://doi.org/10.1090/S0002-9939-1994-1195715-1
- MathSciNet review: 1195715