| 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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| 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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