Toric Geometry and the Semple-Nash modification

Pedro Daniel Gonzalez Perez (1) , Bernard Teissier (2)

1 Departamento de Álgebra [Madrid]
2 IMJ - Institut de Mathématiques de Jussieu

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 eventually resolves the singularities of any toric variety. This solves for toric varieties an old problem of singularity theory.

Mots clés: Toric Geometry; Nash blowing-up; Logarithmic Jacobian ideal

Domaines: Géométrie algébrique [math.AG]

Pedro Daniel Gonzalez Perez, Bernard Teissier. Toric Geometry and the Semple-Nash modification. 2010. ⟨hal-00438184v2⟩