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Valuations Compatible with a Projection

  • Fuensanta Aroca
Conference paper
  • 511 Downloads
Part of the Trends in Mathematics book series (TM)

Abstract

Given an N-dimensional germ of analytic hypersurface \( \mathcal{H} \), a finite projection π : \( \mathcal{H} \to \mathbb{C}^N \) and a valuation v on the ring of convergent series in N variables, we study the valuations on the ring \( \mathcal{O}_\mathcal{H} \) that extend π*v. All these valuations are described when v is a monomial valuation whose weight vector is not orthogonal to any of the faces of the Newton Polyhedron of the discriminant of the projection π. This description is done in terms of the Puiseux parameterizations of \( \mathcal{H} \) with exponents in a cone.

Keywords

Newton Polyhedron valuation discriminant of a projection Puiseux parametrizations 

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References

  1. [1]
    Fuensanta Aroca. Puiseux parametric equations of analytic sets. Proc. Amer. Math., 132:3035–3045, 2004.CrossRefMathSciNetGoogle Scholar
  2. [2]
    M.F. Atiyah and I.G. MacDonald. Introduction to Commutative Algebra. Addison-Wesley series in mathematics. Perseus books, Cambridge, Massachusetts, 1969.zbMATHGoogle Scholar
  3. [3]
    P.D. González Pérez. Singularités quasi-ordinaires toriques et polyèdre de Newton du discriminant. Canad. J. Math., 52(2):348–368, 2000.MathSciNetGoogle Scholar
  4. [4]
    John McDonald. Fiber polytopes and fractional power series. J. Pure Appl. Algebra, 104(2):213–233, 1995.CrossRefMathSciNetGoogle Scholar
  5. [5]
    Paulo Ribenboim. Théorie des valuations. Séminaire de Mathématiques Supérieures de l’Université de Montréal, (Été 1964). Les Presses de l’Université de Montréal, Montreal, Que., 1965.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Fuensanta Aroca
    • 1
  1. 1.Instituto de Matemáticas (Unidad Cuernavaca)Universidad Nacional Autónoma de MéxicoCuernavaca, MorelosMexico

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