2005 Fiscal Year Final Research Report Summary
Complex symplectic varieties and derived categories
| Project/Area Number |
15340008
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Osaka University (2005)
Kyoto University (2003-2004) |
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Principal Investigator |
NAMIKAWA Yoshinori Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80228080)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIKI Akira Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (80027383)
GOTO Ryushi Osaka University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30252571)
USUI Sampei Osaka University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90117002)
OHNO Koji Osaka University, Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (20252570)
SATAKE Ikuo Osaka University, Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (80243161)
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| Project Period (FY) |
2003 – 2005
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| Keywords | derived categories / complex symplectic variety / deformation / Mukai flop / nilpotent orbit / birational geometry |
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| Research Abstract |
1. Mukai flops : (a) We proved that there is an equivalence between derived categories under a Mukai flop. The equivalence is not obtained from the graph of the flop, but from the fiber product. But the same picture is no more true for a G(2,4) flop ; in other words, the functor obtained from the graph of the fiber product is not an equivalence. (b) The nilpotent orbit closure of Complex a simple Lie algebra is a symplectic singularity. All crepant resolutions of such singularities are obtained as the Springer resolutions. In general, the member of crepant resolutions of a singularity is greater than one. We proved that crepant resolutions of such a nilpotent orbit closure are described as a finite sequence of Mukai flops of type A, D and E_6.
2. Deformations of singular symplectic varieties. We proved that, model the minimal under conjecture, the following are equivalent.
(1) a projective symplectic variety Y has a crepant resolutions
(2) a projective symplectic variety Y has a smoothing by a deformations
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