2013 Fiscal Year Final Research Report
Explicit study of rationality of Q-Fano varieties and its related topics
| Project/Area Number |
24840034
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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 | Saga University |
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Principal Investigator |
OKADA Takuzo 佐賀大学, 工学(系)研究科(研究院), 講師 (20547012)
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | ファノ多様体 / 有理性 / 重み付き完全交叉 / 重み付き超曲面 |
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| Research Abstract |
We studied 85 families of Q-Fano 3-fold weighted complete intersections of codimension 2 with the aim to determine their birational Mori fiber structures. As a result, we proved that a general member belonging to 19 families is birationally rigid, and every (quasismooth) member belonging to 14 families has exactly two birational Mori fiber structures. This in particular implies nonrationality of general members belonging to 33 = 19 + 14 families. We also studied 35 families of Q-Fano 3-fold weighted hypersurfaces and determines (non)rationality of generic members belonging to 34 families.
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