Toric Geometry and the Semple-Nash modification
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.
Domaines
Géométrie algébrique [math.AG]
Origine : Fichiers produits par l'(les) auteur(s)