2010 Fiscal Year Final Research Report
Reserch of Fano varieties
| Project/Area Number |
20740005
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TAKAGI Hiromichi 東京大学, 大学院・数理科学研究科, 准教授 (30322150)
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| Project Period (FY) |
2008 – 2011
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| Keywords | ファノ多様体 / カラビヤウ多様体 / べき和多様体 / 偶スピン曲線のモジュライ空間 |
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| Research Abstract |
One result is the research of varieties of power sums with Francesco Zucconi. We discovered a connection between behaviors of rational curves on quintic del Pezzo threefold and the moduli spaces of trigonal even spin curves through varieties of power sums. Our main result in this direction is that we showed the rationality of even spin curves of genus four. Another result is the research of the mirror symmetry and the projective geometry of certain determinantal Calabi-Yau threefolds with Shinobu Hosono.We constructed two types of Calabi-Yau threefolds and showed that they have the same mirror. Moreover, based on this we calculated the BPS numbers of them and interpreted some of them by the projective geometry.
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