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Restriction formula and subadditivity property related to multiplier ideal sheaves

  • Qi’an Guan EMAIL logo and Xiangyu Zhou
Published/Copyright: January 21, 2020

Abstract

We give a restriction formula on jumping numbers which is a reformulation of Demailly–Ein–Lazarsfeld’s important restriction formula for multiplier ideal sheaves and a generalization of Demailly–Kollár’s important restriction formula on complex singularity exponents, and then we establish necessary conditions for the extremal case in the reformulated formula; we pose the subadditivity property on the complex singularity exponents of plurisubharmonic functions which is a generalization of Demailly–Kollár’s fundamental subadditivity property, and then we establish necessary conditions for the extremal case in the generalization. We also obtain two sharp relations on jumping numbers, introduce a new invariant of plurisubharmonic singularities and get its decreasing property for consecutive differences.

Award Identifier / Grant number: NSFC-11431013

Award Identifier / Grant number: NSFC-11825101

Award Identifier / Grant number: NSFC-11522101

Funding statement: The authors were partially supported by NSFC-11431013. The first author was supported by NSFC-11825101 and NSFC-11522101.

Acknowledgements

The authors would like to thank the referees for their helpful and valuable comments.

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Received: 2017-12-05
Revised: 2019-11-20
Published Online: 2020-01-21
Published in Print: 2020-12-01

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