2003/03/17 by Bernard Teissier, Teissier, Bernard · 2 citations
Computer Science · Mathematics · #13A18 #14B05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #math.AG #msc:13A18 #msc:14B05
paper · pdf · doi:10.48550/arxiv.math/0303200
arxiv created 2003/03/17 · openalex publication_date 2003/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A study of the relation between a noetherian local domain with a given valuation and its associated graded ring with respect to the valuation, which in some cases is an esentially toric variety, possibly of infinite embedding dimension, but of finite Krull dimension. After extension of the valuation to a suitable completion (whose existence is not established in the paper) the relation becomes much more precise, and suggests a possible way to establish local uniformization for an excellent equicharacteristic local domain with an algebraically closed residue field, by deforming a partial toric embedded resolution of the essentially toric spectrum of the associated graded ring.