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arXiv · 2609.36420

A Generalized $L^2$ Division Theorem and the Strong Openness Property of Multiplier Ideal Sheaves

Masakazu Takakura
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Abstract

In this paper, we generalize Guan's sharp effective strong openness theorem to the case of several plurisubharmonic weights. The proof uses a generalized Skoda-type $L^2$ division theorem for multiplier ideal sheaves. We also discuss the relationships among the $L^2$-division theorem, the $L^2$-extension theorem and the effective openness theorem.

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Masakazu Takakura. 2026-09-29. A Generalized $L^2$ Division Theorem and the Strong Openness Property of Multiplier Ideal Sheaves. https://arxiv.org/abs/2609.36420

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