Birational geometry for higher-dimensional algebraic varieties

2016 Fiscal Year Final Research Report

• Project/Area Number: 24684002
• Research Category: Grant-in-Aid for Young Scientists (A)
• Allocation Type: Partial Multi-year Fund
• Research Field: Algebra
• 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)
• Project Period (FY): 2012-04-01 – 2017-03-31
• 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

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

Free Research Field

数学、代数幾何学、双有理幾何学、高次元代数多様体論