2013 Fiscal Year Final Research Report
Applications of Frobenius splitting to algebraic geometry
| Project/Area Number |
23740024
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TAKAGI Shunsuke 東京大学, 数理(科)学研究科(研究院), 准教授 (40380670)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 可換環論 / 代数幾何学 / フロベニウス分裂 / F特異点 |
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| Research Abstract |
The goal of this research project was to give an affirmative answer to Schwede-Smith's conjecture, which says that a projective variety X over an algebraically closed field of characteristic zero is log Fano if and only if its modulo p reduction is globally F-regular for sufficiently large p. We proved that the conjecture holds true when X is a Mori dream space or a surface. Under the same assumption, that is, when X is a Mori dream space or a surface, we also proved that if its modulo p reduction is globally F-split for infinitely many p, then X is log Calabi-Yau.
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