Open Access
April 2015 Very good and very bad field generators
Pierrette Cassou-Noguès, Daniel Daigle
Kyoto J. Math. 55(1): 187-218 (April 2015). DOI: 10.1215/21562261-2848160


Let k be a field. A field generator is a polynomial Fk[X,Y] satisfying k(F,G)=k(X,Y) for some Gk(X,Y). If G can be chosen in k[X,Y], we call F a good field generator; otherwise, F is a bad field generator. These notions were first studied by Abhyankar, Jan, and Russell in the 1970s. The present paper introduces and studies the notions of “very good” and “very bad” field generators. We give theoretical results as well as new examples of bad and very bad field generators.


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Pierrette Cassou-Noguès. Daniel Daigle. "Very good and very bad field generators." Kyoto J. Math. 55 (1) 187 - 218, April 2015.


Published: April 2015
First available in Project Euclid: 13 March 2015

zbMATH: 1321.14044
MathSciNet: MR3323532
Digital Object Identifier: 10.1215/21562261-2848160

Primary: 14H50 , 14R10

Keywords: affine plane , birational morphism , dicritical , field generator , plane curve , rational polynomial

Rights: Copyright © 2015 Kyoto University

Vol.55 • No. 1 • April 2015
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