2023/01/25 by Bernard Teissier, Teissier, Bernard H
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2301.10636
openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a complete equicharacteristic noetherian local domain and ν a valuation of its field of fractions whose valuation ring dominates R with trivial residue field extension. The semigroup of values of ν on R∖ \0\ is not finitely generated in general. We produce equations in an appropriate generalized power series ring for the algebra encoding the degeneration of R to the toric graded algebra \rm grνR associated to the filtration defined by ν. We apply this to represent ν as the limit of a sequence of Abhyankar semivaluations (valuations on quotients) of R with finitely generated semigroups.