Valuations Compatible with a Projection

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


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.


Newton Polyhedron valuation discriminant of a projection Puiseux parametrizations 


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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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