Very good and very bad field generators
Algebraic Geometry
2015-11-03 v1 Commutative Algebra
Abstract
Let k be a field. A "field generator" is a polynomial F in k[X,Y] satisfying k(F,G) = k(X,Y) for some G in k(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.
Cite
@article{arxiv.1308.0154,
title = {Very good and very bad field generators},
author = {Pierrette Cassou-Noguès and Daniel Daigle},
journal= {arXiv preprint arXiv:1308.0154},
year = {2015}
}
Comments
27 pages