Newton Transformations and the Motivic Milnor Fiber of a Plane Curve

Pierrette Cassou-Noguès () and Michel Raibaut ()
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Pierrette Cassou-Noguès: Université de Bordeaux, Institut de Mathématiques de Bordeaux, (UMR 5251)
Michel Raibaut: Université Savoie Mont Blanc, CNRS, LAMA, 73000, Université Grenoble Alpes

A chapter in Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, pp 145-189 from Springer

Abstract: Abstract In this article we give an expression of the motivic Milnor fiber at the origin of a polynomial in two variables with coefficients in an algebraically closed field. The expression is given in terms of some motives associated to the faces of the Newton polygons appearing in the Newton algorithm. In the complex setting, we deduce a computation of the Euler characteristic of the Milnor fiber in terms of the area of the surfaces under the Newton polygons encountered in the Newton algorithm which generalizes the Milnor number computation by Kouchnirenko in the isolated case.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-96827-8_7

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DOI: 10.1007/978-3-319-96827-8_7

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