Roles of plurisubharmonic functions
Zhou Xiang Yuab
a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
b HUA Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences
In the present paper, we'll recall the basics of multiplier ideal sheaves and our recent solution of Demailly's strong openness conjecture on multiplier ideal sheaves and related results, and then present some applications in complex geometry, e.g. some new results related to the vanishing, finiteness theorems of analytic cohomology groups with multiplier ideal sheaves for the pseudo-effective line bundles over holomorphically convex manifolds, and generalized Siu's lemma and pseudoeffectiveness of the twisted relative pluricanonical bundles and their direct images.
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