Siu’s lemma: Generalizations and applications

  • Xiangyu Zhou

    Chinese Academy of Sciences, Beijing, China
  • Langfeng Zhu

    Wuhan University, China
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In this survey paper, we present some generalizations of Siu’s lemma related to multiplier ideal sheaves and discuss their applications in some problems related to optimal extension, comparison between singular metrics on exceptional fibers of twisted relative pluricanonical bundles, and subadditivity of Kodaira–Iitaka dimensions with multiplier ideal sheaves. We also discuss some ideas in the proofs.