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

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.

arXiv comment10 pages