| Project/Area Number |
16K17587
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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 |
Geometry
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| Research Institution | Nagoya University (2018-2019)
The University of Tokyo (2016-2017) |
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Principal Investigator |
Imagi Yohsuke 名古屋大学, 多元数理科学研究科, 博士研究員 (30742902)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | calibrated geometry / geometric measure theory / symplectic geometry / スペシャルラグランジアン / 特異点（幾何学的測度論） / 深谷圏 / Special Lagrangians / co-tangent bundles / 基本群 / Harvey Lawson T2 cone / Solvable / Special Lagrangian / 幾何学的測度論 / スペシャルラグランジュ部分多様体 / モジュライ空間 / 特異点 |
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| Outline of Final Research Achievements |
My paper which constructs an example of compact special Lagrangians with a Harvey--Lawson T^2-cone singularity has been published. This paper studies also how the known theorems apply to the example. It is compatible with my on-going project of determining, in that family of special Lagrangians which smoothes the singularity of the example, those with unobstructed Floer cohomology. The smoothing process includes a variation of the ambient Kahler form under which the number of unobstructed special Lagrangians would be conserved; this would be a consequence of the project above.
I have also written, except a certain technical problem, a joint paper with Mohammed Abouzaid. This paper concerns higher multiplicities of special Lagrangians, or more precisely, it considers those special Lagrangians close to a multiple of a given nonsingular special Lagrangian. We do Floer theory for these nearby special Lagrangians, and exclude a branching phenomenon under a hypothesis on the given one.
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| Academic Significance and Societal Importance of the Research Achievements |
Harvey--Lawson T~2-cone特異点を持つスペシャルラグランジアンの一般論は良く解っていたが、例は知られていなかった。一方、シンプレクティック幾何では、正則円盤の数え上げが定めるsuperpotentialの計算はトーリックの場合等にされている。上記のプロジェクトはsuperpotentialの計算例としても面白い。
スペシャルラグランジアンの分岐、higher multiplicityについては純粋に解析的な研究も少しずつ進んでいるが、非存在定理については、上記のようにFloer theoryを使うのが強力である。
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