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, Volume 113, Issue 3, pp 371–382 | Cite as

Newton polygons and families of polynomials

  • Arnaud BodinEmail author


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).


Euler Characteristic Complex Polynomial Continuous Family Generic Fiber Newton Polygon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Laboratoire Paul-PainlevéMathématiquesVilleneuve d’AscqFrance

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