A property of polynomial curves over a field of positive characteristic
HTML articles powered by AMS MathViewer
- by D. Daigle PDF
- Proc. Amer. Math. Soc. 109 (1990), 887-894 Request permission
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.References
- S. S. Abhyankar, Lectures on expansion techniques in algebraic geometry, Tata Institute of Fundamental Research Lectures on Mathematics and Physics, vol. 57, Tata Institute of Fundamental Research, Bombay, 1977. Notes by Balwant Singh. MR 542446
- Shreeram S. Abhyankar and Tzuong Tsieng Moh, Embeddings of the line in the plane, J. Reine Angew. Math. 276 (1975), 148–166. MR 379502
- Richard Ganong, On plane curves with one place at infinity, J. Reine Angew. Math. 307(308) (1979), 173–193. MR 534219, DOI 10.1515/crll.1979.307-308.173
- Richard Ganong, On plane curves with one place at infinity, J. Reine Angew. Math. 307(308) (1979), 173–193. MR 534219, DOI 10.1515/crll.1979.307-308.173
- Richard Ganong, Kodaira dimension of embeddings of the line in the plane, J. Math. Kyoto Univ. 25 (1985), no. 4, 649–657. MR 810969, DOI 10.1215/kjm/1250521013
- Tzuong Tsieng Moh, On the classification problem of embedded lines in characteristic $p$, Algebraic geometry and commutative algebra, Vol. I, Kinokuniya, Tokyo, 1988, pp. 267–279. MR 977764
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 887-894
- MSC: Primary 14H99; Secondary 14E25
- DOI: https://doi.org/10.1090/S0002-9939-1990-1002155-0
- MathSciNet review: 1002155