Birational geometry for higher-dimensional algebraic varieties
Project/Area Number |
24684002
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Research Category |
Grant-in-Aid for Young Scientists (A)
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Allocation Type | Partial Multi-year Fund |
Research Field |
Algebra
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Research Institution | Osaka University (2016) Kyoto University (2012-2015) |
Principal Investigator |
Fujino Osamu 大阪大学, 理学(系)研究科(研究院), 教授 (60324711)
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Project Period (FY) |
2012-04-01 – 2017-03-31
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Project Status |
Completed (Fiscal Year 2016)
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Budget Amount *help |
¥9,100,000 (Direct Cost: ¥7,000,000、Indirect Cost: ¥2,100,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2014: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2013: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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Keywords | 極小モデル理論 / 混合ホッジ構造 / 半対数的j標準対 / 消滅定理 / 半正値性定理 / 擬対数的スキーム / 乗数イデアル層 / 藤田予想 / 半対数的標準対 / 安定多様体 / 飯高不等式 / 数値的小平次元 / アバンダンス予想 / 対数的小平次元 / アフィン多様体 / モジュライ理論 / 混合ホッジ理論 / 射影性 / 高次元代数多様体 / 極小モデル / モジュライ空間 / 半正値性 |
Outline of Final Research Achievements |
I am mainly interested in higher-dimensional complex projective varieties. I established several powerful generalizations of the Kodaira vanishing theorem by using the theory of mixed Hodge structures on cohomology with compact support. As applications, I proved the fundamental theorems of the minimal model theory for semi-log canonical pairs and quasi-log schemes. Moreover, by considering variations of mixed Hodge structures on cohomology with compact support, I obtained a generalization of the Fujita―Zucker―Kawamata semipositivity theorem. As an application, I proved the projectivity of the moduli spaces of stable varieties
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Report
(6 results)
Research Products
(44 results)
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[Presentation] On injectivity and vanishing theorems2016
Author(s)
Osamu Fujino
Organizer
Workshop on $L^2$ Extension theorems
Place of Presentation
Graduate School of Mathematical Sciences, the University of Tokyo
Year and Date
2016-02-16
Related Report
Int'l Joint Research / Invited
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