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Mattias Jonsson; Mircea Mustaţă
Valuations and asymptotic invariants for sequences of ideals
(Valuations et invariants asymptotiques pour les suites graduées d’idéaux.)
Annales de l'institut Fourier, 62 no. 6 (2012), p. 2145-2209, doi: 10.5802/aif.2746
Article PDF | Reviews MR 3060755 | Zbl 1272.14016 | 1 citation in Cedram
Class. Math.: 14F18, 12J20, 14B05
Keywords: Graded sequence of ideals, multiplier ideals, log canonical threshold, valuation

Résumé - Abstract

We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space.

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