Research of the autoequivalence groups of derived categories of algebraic varieties
| Project/Area Number |
18K03249
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
Uehara Hokuto 東京都立大学, 理学研究科, 教授 (80378546)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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)
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| Keywords | 連接層の導来圏 / 代数多様体の分類理論 / 楕円曲面 / Enriques曲面 / 自己同値群 / 三角圏 / 代数曲面 / 導来圏 |
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| Outline of Final Research Achievements |
I studied the derived category of coherent sheaves on algebraic varieties. In particluar, (i) I studied exceptional twists on Enriques surfaces, which is a subspecies of a well-known autoequivalence "spherical twists", (ii) we obtain a solution of Bondal-Polishchuk conjecture for a Hirzebruch surface containg a (-2)-curve, and (iii) I studies Fourier-Mukai partners of elliptic ruled surfaces over arbitrary characteristic fields. In (ii), an affirmative answer for Bondal-Polischuk conjecture was known for del Pezzo surfaces, but we show that it is true for a Hirzebruch surface containg a (-2)-curve, which is an exampe of weak del Pezzo surface.
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| Academic Significance and Societal Importance of the Research Achievements |
連接層の導来圏は代数多様体の重要な不変量として知られており、多元環の表現論、ホモロジカルミラー対称性、代数多様体の分類理論など、広い分野と関係する興味深い研究対象である。連接層の導来圏の研究は、ここ20年で代数幾何学の研究テーマとしても、かなり大きな部分を占めるようになってきたといえる。私は特に、与えれた代数多様体の導来圏の生成元である例外生成列や、導来圏の自己同値群に関して興味を持って調べてきた。これらは、連接層の導来圏の研究の中でも、かなりメジャーなトピックと言え、今後様々な研究に広がっていくと思われる。
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Report
(6 results)
Research Products
(7 results)
