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Analytic multiplier ideals and L^2 extension theorems : 해석적 승수 아이디얼과 L^2 확장 정리
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 김다노 | - |
dc.contributor.author | 서호섭 | - |
dc.date.accessioned | 2019-10-21T03:37:19Z | - |
dc.date.available | 2019-10-21T03:37:19Z | - |
dc.date.issued | 2019-08 | - |
dc.identifier.other | 000000158324 | - |
dc.identifier.uri | https://hdl.handle.net/10371/162409 | - |
dc.identifier.uri | http://dcollection.snu.ac.kr/common/orgView/000000158324 | ko_KR |
dc.description | 학위논문(박사)--서울대학교 대학원 :자연과학대학 수리과학부,2019. 8. 김다노. | - |
dc.description.abstract | In this thesis, multiplier ideal sheaves and L2 extension theorems are main
themes. Multiplier ideals and its jumping numbers play an important role in algebraic geometry and complex geometry because of its applications. Jumping numbers are deeply studied by Ein, Lazardfeld, Smith and Varolin [ELSV] in the algebraic setting. We extend the study of jumping numbers of multiplier ideals due to [ELSV] from the algebraic case to the case of general plurisubharmonic functions. While many properties from [ELSV] are shown to generalize to the plurisubharmonic case, important properties such as periodicity and discreteness do not hold any more. Previously only two particular examples with a cluster point (i.e. failure of discreteness) of jumping numbers were known, due to Guan-Li and to [ELSV] respectively. We generalize them to all toric plurisubharmonic functions in dimension 2 by characterizing precisely when cluster points of jumping numbers exist and by computing all those cluster points. This characterization suggests that clustering of jumping numbers is a rather frequent phenomenon. In particular, we obtain uncountably many new such examples. | - |
dc.description.tableofcontents | Abstract
1 Introduction 1 1.1 Multiplier ideals and jumping numbers 1 1.2 $L^2$ extension theorems: toward inversion of adjunction 6 2 Multiplier ideals and jumping numbers 8 2.1 Multiplier ideals and plurisubharmonic functions 8 2.1.1 Basic notions on plurisubharmonic functions 9 2.1.2 V-equivalence of psh functions 14 2.1.3 Graded systems of ideals and Siu psh functions 15 2.1.4 Toric psh functions and Newton convex bodies 17 2.2 Jumping numbers 20 2.2.1 Definition and basic properties 20 2.2.2 "Mixed" jumping numbers 23 2.3 Periodicity of jumping numbers fails 26 2.4 Cluster points of jumping numbers 29 2.4.1 Cluster points of jumping numbers for toric psh functions 29 2.4.2 Cluster points of jumping numbers for toric psh functions in dimension 2 31 2.5 Appendix by S\'ebastien Boucksom 36 3 $L^2$ extension theorems: toward inversion of adjunction 38 3.1 $L^2$ estimates for the $\overline{\partial}$ operator 38 3.1.1 Basic notions 38 3.1.2 K\"ahler identity and Bochner-Kodaira-Nakano inequality 43 3.1.3 Positivity of vector bundles 47 3.1.4 $L^2$ estimates for the $\overline{\partial}$ operator 48 3.1.5 General $L^2$ estimate theorem for the $\overline{\partial}$ operator 50 3.1.6 $L^2$ extension theorems 54 3.2 Singularities of pairs 58 3.2.1 Basic concepts of singularities of pairs 58 3.2.2 Singularities of pairs and multiplier ideals 61 3.2.3 Inversion of adjunction 65 Abstract (in Korean) 75 Acknowledgement (in Korean) 76 | - |
dc.language.iso | eng | - |
dc.publisher | 서울대학교 대학원 | - |
dc.subject | Jumping Numbers | - |
dc.subject | L^2 Estimates | - |
dc.subject | L^2 Extension Theorem | - |
dc.subject | Analytic Multiplier Ideals | - |
dc.subject.ddc | 510 | - |
dc.title | Analytic multiplier ideals and L^2 extension theorems | - |
dc.title.alternative | 해석적 승수 아이디얼과 L^2 확장 정리 | - |
dc.type | Thesis | - |
dc.type | Dissertation | - |
dc.contributor.department | 자연과학대학 수리과학부 | - |
dc.description.degree | Doctor | - |
dc.date.awarded | 2019-08 | - |
dc.identifier.uci | I804:11032-000000158324 | - |
dc.identifier.holdings | 000000000040▲000000000041▲000000158324▲ | - |
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