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Newton Transformations and the Motivic Milnor Fiber of a Plane Curve

In: Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Author

Listed:
  • 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)

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.

Suggested Citation

  • Pierrette Cassou-Noguès & Michel Raibaut, 2018. "Newton Transformations and the Motivic Milnor Fiber of a Plane Curve," Springer Books, in: Gert-Martin Greuel & Luis Narváez Macarro & Sebastià Xambó-Descamps (ed.), Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, pages 145-189, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-96827-8_7
    DOI: 10.1007/978-3-319-96827-8_7
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