Degenerations of Calabi-Yau manifolds and mirror symmetry
| Project/Area Number |
16K05105
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Gakushuin University |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | カラビ・ヤウ多様体 / ミラー対称性 / 周期積分 / モジュライ空間 / 多変数超幾何微分方程式 / モジュラ―関数 / 複素多様体の変形 / 多変数超幾何方程式 / 双有理幾何学 / 多変数超幾何関数 / 超幾何微分方程式 / モノドロミー / 射影幾何学 / グロモフ・ウィッテン不変量 |
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| Outline of Final Research Achievements |
From the study of string theory in theoretical physics, certain special manifolds, called Calabi-Yau manifolds, were attracted attentions of many researchers, and around 1990, a mysterious symmetry called "mirror symmetry" was discovered in world of Calabi-Yau manifolds. Since the discovery of the mirror symmetry, extensive study toward mathematical understanding of the symmetry has been done. Now, we have two approaches to study the symmetry; one is categorical and the other is geometric method. In this research project, PI has made achievements in constructing explicit and interesting Calabi-Yau manifolds aiming to reveal mirror symmetry. These have been done by developing necessary methods to analyze behavior of some integral called period integral.
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| Academic Significance and Societal Importance of the Research Achievements |
カラビ・ヤウ多様体のミラー対称性は、その発見から３０年近くが経過し、関連する数学の分野に多数の影響を与えてきました。しかしながら、対称性の数学的の完全な理解には至っておらず、現在も不思議な対称性と思われています。このような対称性が現れる興味深いカラビ・ヤウ多様体を構成することは、ミラー対称性を深く理解する上で大切な役割を果たします。また、具体的な例を構築すると同時に、それらを調べる手段・方法を整備して確立することは、ミラー対称性の解明に限らず、派生する様々な数学の問題への応用に寄与するもので、数学の大切な蓄積となります。
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Report
(7 results)
Research Products
(30 results)
