Asymptotic Invariants of Higher Cohomology Groups and Applications to Complex Geometry
| Project/Area Number |
25800051
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Geometry
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| Research Institution | Tohoku University (2015-2016)
Kagoshima University (2013-2014) |
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Principal Investigator |
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| Research Collaborator |
GONGYO Yoshinori 東京大学, 大学院数理科学研究科, 准教授 (70634210)
FUJINO Osamu 大阪大学, 大学院理学研究科, 教授 (60324711)
CAO Junyan Universite Paris 6, Institut de Mathematiques de Jussieu, Analyse complexe et geometrie
DEMAILLY Jean-Pierre Laboratoire de Mathematiques, Institut Fourier
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | ケーラー幾何 / コホモロジー消滅定理 / 正則切断 / 特異計量 / 乗数イデアル層 / 調和積分論 / dbar, L2-理論 / 正値性 / 複素幾何学 / 正則凸多様体 / 高次順像 / 消滅定理 / Bertiniの定理 / 小平次元 / ケーラー多様体 / 随伴束 / dbar-方程式 / L2-理論 / 導来圏 / コホモロジー / 単射性定理 / 豊富性 / 曲率の正値性 |
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| Outline of Final Research Achievements |
From the viewpoint of complex analytic geometry, I studied vanishing theorems of higher cohomology groups that naturally appear in algebraic geometry, and generalized them to (holomorphic) line bundles with singular hermitian metrics. Specifically, I established a Nadel type vanishing theorem for singular hermitian metrics with minimal singularities on big line bundles, and I obtained injectivity theorems to pseudo-effective line bundles by using multiplier ideal sheaves. Furthermore, I generalized them to deformations of Kaehler varieties by using higher direct images. In the processes, I developed techniques of singular hermitian metrics and multiplier ideal sheaves with transcendental singularities and techniques of L2 methods for dbar-equations and the theory of harmonic integrals.
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Report
(5 results)
Research Products
(48 results)
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[Presentation] Analytic methods in algebraic geometry2016
Author(s)
Shin-ichi Matsumura
Organizer
Seminar of Center for Geometry and its Applications
Place of Presentation
Pohang University of Science and Technology, Korea
Year and Date
2016-09-06
Related Report
Int'l Joint Research / Invited
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[Presentation] 多重劣調和関数の近似定理について2015
Author(s)
Shin-ichi Matsumura
Organizer
第50回函数論サマーセミナー 企画特別講演
Place of Presentation
ふれあいセンター(二本松市)
Year and Date
2015-09-04
Related Report
Invited
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