no. 4
Complex analysis
The weighted log canonical threshold
[Le seuil log-canonique pondéré]

Présenté par : Jean-Pierre Demailly

Hiep, Pham Hoang1
1 Department of Mathematics, Hanoi National University of Education, Viet Nam
Comptes Rendus. Mathématique, Tome 352 (2014) no. 4, pp. 283-288.

Dans cet article, nous montrons comment appliquer la version originelle du théorème d'extension L2 de Ohsawa et Takegoshi à la base standard d'un faisceau d'idéaux multiplicateurs associé à une fonction plurisousharmonique. Ceci nous permet de redémontrer la conjecture d'ouverture forte et d'obtenir une version effective du théorème de semi-continuité pour les seuils log-canoniques pondérés.

In this note, we show how to apply the original L2-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong openness conjecture and to obtain an effective version of the semicontinuity theorem for weighted log canonical thresholds.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.02.010
Hiep, Pham Hoang 1

1 Department of Mathematics, Hanoi National University of Education, Viet Nam 
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Hiep, Pham Hoang. The weighted log canonical threshold. Comptes Rendus. Mathématique, Tome 352 (2014) no. 4, pp. 283-288. doi : 10.1016/j.crma.2014.02.010. http://www.numdam.org/articles/10.1016/j.crma.2014.02.010/

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