The weighted log canonical threshold

Hiep, Pham Hoang

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 $L^2$ 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 $L^2$-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.

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