English

On the minimal compactification of a polynomial in two variables

Algebraic Geometry 2007-05-23 v3

Abstract

Consider a primitive polynomial ff in two variables, thought of as a map from the affine plane to the affine line. We study the minimimal compactification of ff; from our result one deduces in particular that if one of the fibers of ff has only one fiber at infinity, then all the fibers of ff 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.

Keywords

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

R2 v1 2026-07-22T18:02:34.297Z