2015 Fiscal Year Final Research Report
Calabi-Yau threefolds in positive characteristic and related problems
| Project/Area Number |
25400056
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Keywords | Calabi-Yau多様体 / 正標数 / 小平消滅定理 / 持ち上げ可能性 |
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| Outline of Final Research Achievements |
I proved that a Kodaira type vanishing theorem for the first cohomology holds for non-liftable Calabi-Yau threefolds in positive characteristic for the existing examples such as the Hirokado's example in 1999 and the Schroeer's example of 2003. Moreover, it is proved that this kind of vanishing holds for Calabi-Yau 3-folds with no p-torsion in the Picard varieties.
Also I constructed a non-simply connected non-liftable Calabi-Yau threefold in positive characteritic. This example is produced from the Schroeer's example using a method ispired by an idea of Arnaud Beauville.
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| Free Research Field |
代数幾何
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