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Newton polygons and families of polynomials

Arnaud Bodin
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Abstract

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 $μ(s)+λ(s)$ 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 $\Cc^2$).

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Arnaud Bodin. 2004-01-26. Newton polygons and families of polynomials. https://doi.org/10.1007/s00229-004-0440-6

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