Toric geometry and the Semple-Nash modification

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...

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Detalles Bibliográficos
Autores: González Pérez, Pedro Daniel, Teissier, Bernard
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33248
Acceso en línea:https://hdl.handle.net/20.500.14352/33248
Access Level:acceso abierto
Palabra clave:512.7
Toric geometry
Semple-Nash modification
Logarithmic jacobian ideal
Geometria algebraica
1201.01 Geometría Algebraica
Descripción
Sumario: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 it is shown that over an algebraically closed base field of zero characteristic the Semple-Nash modification of a general toric variety is isomorphic to the blowing up of the sheaf of logarithmic jacobian ideals and that in any characteristic this blowing-up is an isomorphism if and only if the toric variety is non singular.