Toric Geometry and the Semple-Nash modification

Details Toric Geometry and the Semple-Nash modification Toric Geometry and the Semple-Nash modification

2009-12-03

arxiv.org/abs/0912.0593v4

Mathematics

Algebraic Geometry

Correction of previous versions after the detection of errors by Professor Michael Thaddeus

Scientific paper

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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