2011 Fiscal Year Final Research Report
Birational geometry of higher-dimensional algebraic varieties higher-dimensional algebraic
| Project/Area Number |
20684001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
FUJINO Osamu 京都大学, 大学院・理学研究科, 准教授 (60324711)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 極小モデル / 消滅定理 / アバンダンス予想 / 標準束公式 / トーリック幾何学 / 混合ホッジ構造 |
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| Research Abstract |
I mainly studied the birational geometry of higher-dimensional algebraic varieties. I obtained various vanishing theorems by using the theory of mixed Hodge structures. By these new vanishing theorems, I established the fundamental theorems of the minimal model theory for log canonical pairs. I also studied the abundance conjecture, isolated log canonical singularities, variations of mixed Hodge structure, and so on. In addition to the above mentioned studies, I am interested in the toric geometry, singular algebraic surfaces, generalizations of Kodaira's canonical bundle formula, and so on.
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