2010 Fiscal Year Final Research Report
Research on pluricanonical bundles and multiplier ideal sheaves for a degenerate family of complex manifolds
| Project/Area Number |
19340014
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HIRACHI Kengo 東京大学, 大学院・数理科学研究科, 教授 (60218790)
KONNO Rihoshi 東京大学, 大学院・数理科学研究科, 准教授 (20254138)
TAKAGI Shunsuke 東京大学, 大学院・数理科学研究科, 准教授 (40380670)
OHSAWA Takeo 名古屋大学, 大学院・多元数理科学研究科, 教授 (30115802)
MABIUCHI Toshiki 大阪大学, 大学院・理学研究科, 教授 (10112278)
SATO Eiichi 九州大学, 大学院・数理科学研究院, 教授 (10112278)
HAYASHIMOTO Atsushi 国立長野高専, 一般科, 准教授 (90342493)
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| Research Collaborator |
MOUROUGANE Christophe フランスレンヌ大学, 教授
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| Project Period (FY) |
2007 – 2010
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| Keywords | 多重標準束 / 乗数イデアル層 / 退化族 / ホッジ計量 |
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| Research Abstract |
For a smooth proper Kaehler morphism f : X→Y and a Nakano semi-positive vector bundle(E, h) on X, we showed that every direct image sheaf R^qf_* K_{ X/Y}(E) is locally free and that it is equipped with a natural Hermitian metric, called a Hodge metric, with Nakano semi-positive curvature. Moreover even when f : X→Y can be singular, we showed that the positivity of a direct image sheaf extends across the singular locus of f on Y.
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