2022 Fiscal Year Final Research Report
Geometry and topology of torus actions and combinatorics
Project/Area Number |
19K03472
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 11020:Geometry-related
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Research Institution | Osaka Metropolitan University (2022) Osaka City University (2019-2021) |
Principal Investigator |
Masuda Mikiya 大阪公立大学, 大学院理学研究科, 特任教授 (00143371)
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Project Period (FY) |
2019-04-01 – 2023-03-31
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Keywords | Toric Topology / convex polytope / torus orbit closure / flag variety / Hessenberg variety |
Outline of Final Research Achievements |
I continued joint work with Eunjeong Lee and Seonjeong Park on the geometry and topology of torus orbit closures in the flag variety and related combonatorics. In particular, we wrote a survey article on this topis as a chapter of the Handbook of Combinatorial Algebraic Geometry: Subvarieties ofthe Flag Variety. I also worked with Takashi Sato on the cohomology ring of a regular semisimple Hessenberg variety. The ultimate goal of this work is to prove a long standing Stanley-Stembridge conjecture in graph theory affirmatively.
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Free Research Field |
Topology
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Academic Significance and Societal Importance of the Research Achievements |
旗多様体におけるトーラス軌道の閉包の研究は,1980年代にGelfand-Serganova, Kryachko らによって初められた.その後,トーラス軌道の閉包の特異性など調べられているが,トポロジーに関しては研究されていなかったように思われる.我々は,旗多様体におけるSchubert variety もっと一般に Richardson variety における一般的なトーラス軌道の閉包の幾何・トポロジーと組合せ論の関係を調べた.これは今後の研究の礎になると期待している.
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