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...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2014 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/33248 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/33248 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.7 Toric geometry Semple-Nash modification Logarithmic jacobian ideal Geometria algebraica 1201.01 Geometría Algebraica |
| Resumo: | 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. |
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