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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A property of polynomial curves over a field of positive characteristic


Author: D. Daigle
Journal: Proc. Amer. Math. Soc. 109 (1990), 887-894
MSC: Primary 14H99; Secondary 14E25
MathSciNet review: 1002155
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Abstract: Let $ {\mathbf{k}}$ be an algebraically closed field of characteristic $ p > 0$. We show that if $ F \in {\mathbf{k}}\left[ {X,Y} \right]$ is a rational curve with one place at infinity and with nonprincipal bidegree, such that $ \theta \left( F \right) \in {\mathbf{k}}\left[ {{X^p},Y} \right]$ for some automorphism $ \theta $ of $ {\mathbf{k}}\left[ {X,Y} \right]$, then $ \theta $ can be chosen to be either linear or of "de Jonquière" type. We also give consequences of that fact for the problem of classifying the embeddings of the line in the plane.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1002155-0
PII: S 0002-9939(1990)1002155-0
Article copyright: © Copyright 1990 American Mathematical Society