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Toric geometry and the Semple-Nash modification



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González Pérez, Pedro Daniel and Teissier, Bernard (2014) Toric geometry and the Semple-Nash modification. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A: Matemáticas, 108 (1). pp. 1-48. ISSN 1578-7303


Official URL: http://link.springer.com/article/10.1007/s13398-012-0096-0


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.

Item Type:Article
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Special issue for the Tordesillas Conference in honor of H. Hironaka's 80th Birthday

Uncontrolled Keywords:Toric geometry, Semple-Nash modification, Logarithmic jacobian ideal
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:12720
Deposited On:20 May 2011 11:37
Last Modified:05 Sep 2019 07:35

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