2018 Fiscal Year Annual Research Report
Boundedness of Fano varieties
| Project/Area Number |
16K17558
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| Research Institution | The University of Tokyo |
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Principal Investigator |
江 辰 東京大学, カブリ数物連携宇宙研究機構, 特任研究員 (90772773)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Fano varieties / Calabi-Yau varieties / boundedness / general type / geography problem |
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| Outline of Annual Research Achievements |
In FY2018, I continued my study related to the boundedness of Fano varieties.
Working with collaborators, we used the methods in the study of boundedness of Fano varieties to study boundedness of rationally connected Calabi-Yau varieties, which are varieties with some similar properties with Fano varieties. We showed that rationally connected Calabi-Yau 3-folds with klt singularities form a birationally bounded family, and they form a bounded family modulo flops assuming mld’s are bounded away from 1.
Working with collaborators, we considered geography problem for varieties of general type and proved an optimal Noether inequality for 3-folds of general type. Surprisingly, methods used for Fano varieties such as global log canonical thresholds and connectedness lemma are involved and become keys to the final solution of the problem.
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Research Products
(6 results)
