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Toric geometry and the Semple-Nash modification

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0912.0593.pdf (546.75 KB)
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http://link.springer.com/article/10.1007/s13398-012-0096-0
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Publication Date
2014-10
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Real Academia Ciencias Exactas Físicas Y Naturales
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Abstract
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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Special issue for the Tordesillas Conference in honor of H. Hironaka's 80th Birthday
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Geometria algebraica
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1201.01 Geometría Algebraica
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https://hdl.handle.net/20.500.14352/33248
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