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.
Funding source: National Natural Science Foundation of China
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.
References
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Restriction formula and subadditivity property related to multiplier ideal sheaves
- Proper Lie groupoids are real analytic
- Deformations of rational curves in positive characteristic
- Curved Rickard complexes and link homologies
- Boundary properties of fractional objects: Flexibility of linear equations and rigidity of minimal graphs
Articles in the same Issue
- Frontmatter
- Restriction formula and subadditivity property related to multiplier ideal sheaves
- Proper Lie groupoids are real analytic
- Deformations of rational curves in positive characteristic
- Curved Rickard complexes and link homologies
- Boundary properties of fractional objects: Flexibility of linear equations and rigidity of minimal graphs