On the minimal compactification of a polynomial in two variables
Abstract
Consider a primitive polynomial $f$ in two variables, thought of as a map from the affine plane to the affine line. We study the minimimal compactification of $f$; from our result one deduces in particular that if one of the fibers of $f$ has only one fiber at infinity, then all the fibers of $f$ have a simultaneous resolution of singularities at infinity. From this one gets a very simple proof of the SuzukiAbhyankarMoh theorem on the embeddings of the affine line in the plane.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 1999
 arXiv:
 arXiv:math/9904035
 Bibcode:
 1999math......4035V
 Keywords:

 Algebraic Geometry
 EPrint:
 Plain TeX, 5 pages. Added some references