Algebraic bounds on analytic multiplier ideals
[Limites algébriques sur les idéaux multiplicateurs analytiques]
Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1077-1108.

Pour un diviseur pseudo-effectif L nous construisons l’idéal diminué 𝒥 σ (L) qui est une extension “continue” de l’idéal multiplicateur asymptotique pour les grands diviseurs au cône pseudo-effectif. L’idéal multiplicateur d’une métrique hermitiennes à singularités minimales sur 𝒪 X (L) est souvent contenu dans 𝒥 σ (L). Nous caractérisons les diviseurs abondants par l’idéal diminué, montrant que les informations de nature géométriques et analytique doivent coïncider.

Given a pseudo-effective divisor L we construct the diminished ideal 𝒥 σ (L), a “continuous” extension of the asymptotic multiplier ideal for big divisors to the pseudo-effective boundary. Our main theorem shows that for most pseudo-effective divisors L the multiplier ideal 𝒥(h min ) of the metric of minimal singularities on 𝒪 X (L) is contained in 𝒥 σ (L). We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.

DOI : https://doi.org/10.5802/aif.2874
Classification : 14C20
Mots clés : idéal multiplicateur, métrique à singularités minimales
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Lehmann, Brian. Algebraic bounds on analytic multiplier ideals. Annales de l'Institut Fourier, Tome 64 (2014) no. 3, pp. 1077-1108. doi : 10.5802/aif.2874. http://www.numdam.org/articles/10.5802/aif.2874/

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