Study of Lagrangian fibrations via projective embeddings
Project/Area Number |
19740025
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Geometry
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Research Institution | Tohoku University |
Principal Investigator |
NOHARA Yuichi Tohoku University, 教育学部, 講師 (60447125)
|
Project Period (FY) |
2007 – 2010
|
Project Status |
Completed (Fiscal Year 2010)
|
Budget Amount *help |
¥3,730,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000)
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Keywords | ラグランジアンファイブレーション / 完全可積分系 / ミラー対称性 / トーリック退化 / Grassmann多様体 / Gelfand-Cetlin系 / Gelfand-Cetlin型 / ポテンシャル関数 / 幾何学 / 幾何学的量子化 |
Research Abstract |
I have proved that the Gelfand-Cetlin system, a completely integrable system on a flag manifold of type A, can be deformed into a toric moment map on a toric variety (this is a joint work with T. Nishinou and K. Ueda). As an application we computed the potential functions of the Lagrangian torus fibers of the Gelfand-Cetlin system, and showed that it coincides with the superpotential of the Landau-Ginzburg mirror of the flag manifold. It is known that toric degenerations of a Grassmannian of two-planes in a complex vector space are classified by certain trees. For each such tree I have constructed a completely integrable system on the Grassmannian, and proved that it can be deformed into a toric moment map under the corresponding toric degeneration. This result implies that completely integrable systems on a polygon space constructed by Kapovich and Millson also admit deformations into toric moment maps. I have also studied a relation between Kapovich-Milson's integrable systems and Goldman's integrable systems on a moduli space of parabolic bundles of rank 2 on a projective line.
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Report
(6 results)
Research Products
(50 results)