Valuations and asymptotic invariants for sequences of ideals
Annales de l'Institut Fourier, Volume 62 (2012) no. 6, pp. 2145-2209.

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.

On étudie les nombres de saut asymptotiques pour les suites graduées d’idéaux et on démontre que ces invariants se calculent par une valuation réelle définie sur un corps de fonctions. Nous conjecturons que toute valuation qui calcule un tel nombre de saut est nécessairement quasi-monomiale. Cette conjecture est vraie en dimension deux. En général, on réduit la conjecture au cas de l’espace affine et des suites graduées d’idéaux de valuations. Au passage on étudie la structure d’un espace adéquat de valuations.

DOI: 10.5802/aif.2746
Classification: 14F18, 12J20, 14B05
Keywords: Graded sequence of ideals, multiplier ideals, log canonical threshold, valuation
Mot clés : Suite graduée d’idéaux, idéaux multiplicateurs, seuil log canonique, valuation.
Jonsson, Mattias 1; Mustaţă, Mircea 1

1 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
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Jonsson, Mattias; Mustaţă, Mircea. Valuations and asymptotic invariants for sequences of ideals. Annales de l'Institut Fourier, Volume 62 (2012) no. 6, pp. 2145-2209. doi : 10.5802/aif.2746. http://www.numdam.org/articles/10.5802/aif.2746/

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