On the minimal compactification of a polynomial in two variables
Algebraic Geometry
2007-05-23 v3
Abstract
Consider a primitive polynomial in two variables, thought of as a map from the affine plane to the affine line. We study the minimimal compactification of ; from our result one deduces in particular that if one of the fibers of has only one fiber at infinity, then all the fibers of have a simultaneous resolution of singularities at infinity. From this one gets a very simple proof of the Suzuki-Abhyankar-Moh theorem on the embeddings of the affine line in the plane.
Cite
@article{arxiv.math/9904035,
title = {On the minimal compactification of a polynomial in two variables},
author = {Angelo Vistoli},
journal= {arXiv preprint arXiv:math/9904035},
year = {2007}
}
Comments
Plain TeX, 5 pages. Added some references