Analytic spread of filtrations on two dimensional normal local rings
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Publication:6393442
DOI10.1017/NMJ.2022.35arXiv2203.05935MaRDI QIDQ6393442
Publication date: 11 March 2022
Abstract: In this paper we prove that a classical theorem by McAdam about the analytic spread of an ideal in a Noetherian local ring continues to be true for divisorial filtrations on a two dimensional normal excellent local ring , and that the Hilbert polynomial of the fiber cone of a divisorial filtration on has a Hilbert function which is the sum of a linear polynomial and a bounded function. We prove these theorems by first studying asymptotic properties of divisors on a resolution of singularities of the spectrum of . The filtration of the symbolic powers of an ideal is an example of a divisorial filtration. Divisorial filtrations are often not Noetherian, giving a significant difference in the classical case of filtrations of powers of ideals and divisorial filtrations.
Singularities in algebraic geometry (14B05) Valuations and their generalizations for commutative rings (13A18) Local structure of morphisms in algebraic geometry: étale, flat, etc. (14B25)
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