English

Generally rational polynomials in two variables

Algebraic Geometry 2013-07-16 v1

Abstract

Let k be an algebraically closed field. A polynomial F in k[X,Y] is said to be "generally rational" if, for almost all c in k, the curve " F= c '' is rational. It is well known that, if char(k)=0, F is generally rational iff there exists G in k(X,Y) such that k(F,G)=k(X,Y). We give analogous results valid in arbitrary characteristic.

Keywords

Cite

@article{arxiv.1307.3752,
  title  = {Generally rational polynomials in two variables},
  author = {Daniel Daigle},
  journal= {arXiv preprint arXiv:1307.3752},
  year   = {2013}
}

Comments

17 pages

R2 v1 2026-06-22T00:51:09.091Z