Newton polygons and families of polynomials

2003/05/31 by Arnaud Bodin
Mathematics · #math.AG #math.GT #msc:32S20 #msc:14M25

paper · pdf · doi:10.1007/s00229-004-0440-6

published as manuscripta mathematica (2004, vol. 113, 371-382) · 12 pages, 8 figures. Final version, to appear in Manuscripta Mathematica

arxiv created 2004/01/26 · arxiv updated 2009/11/30

Abstract

We consider a continuous family (f_s), s∈[0,1] of complex polynomials in two variables with isolated singularities, that are Newton non-degenerate. We suppose that the Euler characteristic of a generic fiber is constant (or equivalently the sum of the affine Milnor number and the Milnor number at infinity μ(s)+λ(s) is constant). We firstly prove that the set of critical values at infinity depends continuously on s, and secondly that the degree of the f_s is constant (up to an algebraic automorphism of \Cc²).

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