On the minimal compactification of a polynomial in two variables
Angelo Vistoli
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 Suzuki-Abhyankar-Moh theorem on the embeddings of the affine line in the plane.
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