Un exemple effectif de gradué non noethérien associé à une valuation divisorielle. (An effective example of a non noetherian graduate ring associated to a divisorial valuation)

DOI10.5802/aif.1748zbMath0966.13001OpenAlexW2324228734MaRDI QIDQ1965854

Olivier Piltant, Carlos Galindo Pastor, Vincent Cossart

Publication date: 1 March 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_1_105_0

zbMATH Keywords

Poincaré serieslocal regular ringdivisorial valuationnot Noetherian graded algebra

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Valuations and their generalizations for commutative rings (13A18) Valuation rings (13F30) Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics (13A30) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items (11)

A divisorial valuation with irrational volume. ⋮ Multiplicities and Mixed Multiplicities of Filtrations ⋮ Semigroups of valuations on local rings ⋮ On divisors computing MLD's and LCT's ⋮ Examples of multiplicities and mixed multiplicities of filtrations ⋮ On Finite and Nonfinite Generation of Associated Graded Rings of Abhyankar Valuations ⋮ Divisorial valuations via arcs ⋮ Semigroup and Poincaré series for a finite set of divisorial valuations ⋮ The total coordinate ring of a smooth projective surface ⋮ The Minkowski equality of filtrations ⋮ Mixed multiplicities of divisorial filtrations

Cites Work

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• Semifactoriality and Muhly's condition (N) in two dimensional local rings
• On a problem of Zariski on dimensions of linear systems
• The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface
• Valuations in Function Fields of Surfaces
• Genre des courbes de l'espace projectif. II

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