Toric geometry and the Semple–Nash modification

Original Paper

Abstract

This paper proposes some material towards a theory of general toric varieties without the assumption of normality. Their combinatorial description involves a fan to which is attached a set of semigroups subjected to gluing-up conditions. In particular it contains a combinatorial construction of the blowing up of a sheaf of monomial ideals on a toric variety. In the second part this is used to show that iterating the Semple–Nash modification or its characteristic-free avatar provides a local uniformization of any monomial valuation of maximal rank dominating a point of a toric variety.

Keywords

Toric geometry Semple–Nash modification Logarithmic Jacobian ideal 

Mathematics Subject Classification (2000)

14M25 14E15 14B05 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Instituto de Ciencias Matemáticas-CSIC-UAM-UC3M-UCM. Dpto. de Algebra. Facultad de Ciencias MatemáticasUniversidad Complutense de MadridMadridSpain
  2. 2.Institut Mathématique de Jussieu, UMR 7586 du CNRSParisFrance

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