2010 Fiscal Year Final Research Report
Birational geometry of nonrational rationally connected varieties
| Project/Area Number |
21840032
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
OKADA Takuzo Kyoto University, 数理解析研究所, 特定研究員(グローバルCOE) (20547012)
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| Project Period (FY) |
2009 – 2010
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| Keywords | 有理連結多様体 / ファノ多様体 / 双有理的非有界性 |
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| Research Abstract |
Q-Fano varieties appear as one of the final outcomes of the (log) minimal model program and they are important objects in the classification theory of algebraic varieties. We studied the birational unboundedness of higher-dimensional Q-Fano varieties. The birational unboundedness means that varieties in concern form infinitely many families even if we identify varieties which are birational to each other. We have proved the birational unboundedness of Q-Fano varieties in each dimension at least 3. We further proved a similar result for rationally connected Mori fiber spaces.
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