Derived categories related to the McKay correcepondence and Homological Mirror Symmetry
| Project/Area Number |
23340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
Uehara Hokuto 首都大学東京, 理工学研究科, 准教授 (80378546)
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| Co-Investigator(Kenkyū-buntansha) |
TODA Yukinobu 東京大学, 国際高等研究所Kavli数物連携宇宙機構, 准教授 (20503882)
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| Project Period (FY) |
2011-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2015: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Keywords | 導来圏 / トーリック多様体 / 楕円曲面 / 連接層の導来圏 / Bridgelandの安定性条件 / マッカイ対応 / トーリック スタック |
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| Outline of Final Research Achievements |
We studied the derived categories of coherent sheaves on algebraic varieties from many aspects. We obtained (1) a counterexample to birational Torelli problem, (2) full exceptional collections on toric varieties by Frobenius morphisms, (3) a classification of exceptional sheaves on a Hirzebruch surface and (4) a description of the autoequivalences groups on minimal elliptic surfaces. We applied our study on Fourier--Mukai partners on elliptic surfaces to obtain (1). The result (2) is a generalization of the McKay correspondence. The study in (4) should be generalized in the cases of any algebraic surfaces.
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Report
(6 results)
Research Products
(17 results)
