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 be an algebraically closed field of characteristic . We show that if is a rational curve with one place at infinity and with nonprincipal bidegree, such that for some automorphism of , then 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.

**[1]**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****[2]**Shreeram S. Abhyankar and Tzuong Tsieng Moh,*Embeddings of the line in the plane*, J. Reine Angew. Math.**276**(1975), 148–166. MR**0379502****[3]**Richard Ganong,*On plane curves with one place at infinity*, J. Reine Angew. Math.**307/308**(1979), 173–193. MR**534219**, 10.1515/crll.1979.307-308.173**[4]**Richard Ganong,*On plane curves with one place at infinity*, J. Reine Angew. Math.**307/308**(1979), 173–193. MR**534219**, 10.1515/crll.1979.307-308.173**[5]**Richard Ganong,*Kodaira dimension of embeddings of the line in the plane*, J. Math. Kyoto Univ.**25**(1985), no. 4, 649–657. MR**810969****[6]**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**

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DOI:
https://doi.org/10.1090/S0002-9939-1990-1002155-0

Article copyright:
© Copyright 1990
American Mathematical Society