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Pré-Publication, Document De Travail Année : 2009

Toric Geometry and the Semple-Nash modification

Bernard Teissier

Résumé

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.
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Dates et versions

hal-00438184 , version 1 (02-12-2009)
hal-00438184 , version 2 (05-02-2010)
hal-00438184 , version 3 (09-07-2010)
hal-00438184 , version 4 (18-02-2013)

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Pedro Daniel Gonzalez Perez, Bernard Teissier. Toric Geometry and the Semple-Nash modification. 2009. ⟨hal-00438184v1⟩
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