Newton polygons and families of polynomials

Details Newton polygons and families of polynomials Newton polygons and families of polynomials

2003-05-27

arxiv.org/abs/math/0305377v3

manuscripta mathematica (2004, vol. 113, 371-382)

Mathematics

Algebraic Geometry

12 pages, 8 figures. Final version, to appear in Manuscripta Mathematica

Scientific paper

10.1007/s00229-004-0440-6

We consider a continuous family $(f_s)$, $s\in[0,1]$ 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 $\mu(s)+\lambda(s)$ 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 $\Cc^2$).

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