2014 Fiscal Year Final Research Report
A study on higher dimensional Fano manifolds using the minimal model theory with scaling
| Project/Area Number |
23740028
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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 | Tokai University |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Keywords | ファノ多様体 |
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| Outline of Final Research Achievements |
We studied higher dimensional Fano manifolds using the theory of extremal contractions. We gave examples of Fano manifolds with small contractions and investigated their property. It is known that by the successive blow-up along a curve and a subvariety of codimension 2, we can get projective varieties with small contractions. We have considered Fano manifolds obtained by this construction. The case of blow-ups of the products of projective spaces are studied in detail. On the other hand, we study on the number of irreducible components of exceptional sets of small contractions. In a special case, we obtained a sufficient condition for this number to be one.
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| Free Research Field |
代数幾何学
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