Algebraic bounds on analytic multiplier ideals

[Limites algébriques sur les idéaux multiplicateurs analytiques]

Lehmann, Brian

Annales de l'Institut Fourier, Tome 64 (2014), p. 1077-1108 / Harvested from Numdam

Résumé

Pour un diviseur pseudo-effectif $L$ nous construisons l’idéal diminué $\mathcal{J}_{\sigma }(L)$ 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 $\mathcal{O}_{X}(L)$ est souvent contenu dans $\mathcal{J}_{\sigma }(L)$. Nous caractérisons les diviseurs abondants par l’idéal diminué, montrant que les informations de nature géométriques et analytique doivent coïncider.

Abstract

Given a pseudo-effective divisor $L$ we construct the diminished ideal $\mathcal{J}_{\sigma }(L)$, 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 $\mathcal{J}(h_{\textrm{min}})$ of the metric of minimal singularities on $\mathcal{O}_{X}(L)$ is contained in $\mathcal{J}_{\sigma }(L)$. We also characterize abundant divisors using the diminished ideal, indicating that the geometric and analytic information should coincide.

Détail

Publié le : 2014-01-01

MR 3330164 | Zbl 06387301

DOI : https://doi.org/10.5802/aif.2874
Classification:  14C20
Mots clés: idéal multiplicateur, métrique à singularités minimales

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