Fulger, Mihai
Local volumes of Cartier divisors over normal algebraic varieties  [ Volumes locaux de diviseurs de Cartier sur des variétés algébriques normales ]
Annales de l'institut Fourier, Tome 63 (2013) no. 5 , p. 1793-1847
MR 3186509 | Zbl 1297.14015
doi : 10.5802/aif.2815
URL stable : http://www.numdam.org/item?id=AIF_2013__63_5_1793_0

Classification:  14E05,  14E15,  14B05,  14B15,  32S05
Mots clés: Volumes locaux, multiplicité de Hilbert-Samuel, plurigenres, invariants asymptotiques, corps de Okounkov
Dans cet article, nous étudions une notion de volume local pour les diviseurs de Cartier sur des éclatements arbitraires de variétés algébriques complexes normales de dimension supérieure à un, avec un point distingué. Nous appliquons cela pour étudier un invariant de singularités isolées normales, en généralisant un volume défini par J. Wahl dans le cas des surfaces. Nous comparons également cet invariant à celui obtenu dans les travaux récents de T. de Fernex, S. Boucksom, et C. Favre.
In this paper we study a notion of local volume for Cartier divisors on arbitrary blow-ups of normal complex algebraic varieties of dimension greater than one, with a distinguished point. We apply this to study an invariant for normal isolated singularities, generalizing a volume defined by J. Wahl for surfaces. We also compare this generalization to a different one arising in recent work of T. de Fernex, S. Boucksom, and C. Favre.

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