Newton polygons and families of polynomials
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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. 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 ℂ2).
KeywordsEuler Characteristic Complex Polynomial Continuous Family Generic Fiber Newton Polygon
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