Toric geometry and the Semple–Nash modification
By P. D. González Pérez, B. Teissier. RACSAM, 2009
56 citations recorded by the source corpus.
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 this is used to show that iterating the Semple–Nash modification or its characteristic-free avatar provides a local uniformization of any monomial valuation of maximal rank dominating a point of a toric variety.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/b4c9dc57ab0019a5e174bc4815811612e8524485
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In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
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Citations in the corpus
- On fields of totally $\mathfrak{S}$-adic numbers. With an appendix by Florian Pop (2012, background): “By construction, (since it is the blowing-up of a monomial ideal, see [34], part 1, section 5) and there is no relation between the values of the variables there exist an element m ∈ Γ0 and a system of generators (δ j ) of the semigroup Γ0 of the values of ν0 on R e 0 such that m + δ e j ∈ Γ0 for al”