2019 Fiscal Year Final Research Report
Study on flag domains and its application to Hodge theory
| Project/Area Number |
16K17576
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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 |
Algebra
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| Research Institution | Senshu University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 旗領域 / 対称空間 / リー理論 |
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| Outline of Final Research Achievements |
An open real group orbit in a complex flag manifold is called a flag domain. In this research project, we studied geometric properties of flag domains. One of the main result is about pseudoconcavity of flag domains. We proved that a flag domain is either pseudoconvex or pseudoconcave, which is positive confirmation of Huckleberry's conjecture. The paper on this result has been published in Mathematische Annalen as a co-authored paper with Huckleberry and Latif. Moreover, we studied cycle-connectivity of pseudoconcave flag domains. We determined which pseudoconcave flag domain is one-connected in some particular cases.
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| Free Research Field |
複素幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
この研究成果によりAlan Huckleberry氏が過去の論文で立てた予想が肯定的に解決され，旗領域に関する理解が進んだ．またその成果は国際研究雑誌に掲載され，様々な研究機関で講演を行った．
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