González Pérez, Pedro DanielTeissier, Bernard2023-06-192023-06-192014-101578-730310.1007/s13398-012-0096-0https://hdl.handle.net/20.500.14352/33248Special issue for the Tordesillas Conference in honor of H. Hironaka's 80th BirthdayThis 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.engjournal articlehttp://link.springer.com/article/10.1007/s13398-012-0096-0http://www.springer.com/http://arxiv.org/pdf/0912.0593.pdfopen access512.7Toric geometrySemple-Nash modificationLogarithmic jacobian idealGeometria algebraica1201.01 Geometría Algebraica