Toric Structure of the Graded Algebra Relative to a Valuation

Antonio Campillo and Carlos Galindo

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 219-234 from Springer

Abstract: Abstract Throughout this paper, v will denote a valuation of the quotient field F of a Noetherian local domain (R, M). Also, we shall assume that v is centered at R. Denote by K the residue field of R and by S (:= v(R\{0}) the value semigroup of v. For each m ∈ S, set P m (P m + ) := { F ∈ R|v(f ≥ (>) m}). P m and P m + are ideals of R and we call the graded algebra of R relative to v to the S-graded K-algebra $$ gr_v R = \mathop \oplus \limits_{m \in S} P_m /P_{^m }^ + . $$

Keywords: Simplicial Complex; Local Ring; Toric Variety; Free Resolution; Vector Space Complex (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-18487-1_12

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DOI: 10.1007/978-3-642-18487-1_12

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