2023 Fiscal Year Final Research Report
Moduli of coherent sheaves and complexes
| Project/Area Number |
18H01113
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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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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kobe University |
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Principal Investigator |
Yoshioka Kota 神戸大学, 理学研究科, 教授 (40274047)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Keywords | K3曲面、Enriques曲面 / アーベル曲面 / Brill-Noether / 安定層 |
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| Outline of Final Research Achievements |
I studied the birational geometry of stable sheaves on Enriques surfaces. In particular, with Howard Nuer, I proved that the moduli of odd rank stable sheaves is birationally equivalent to the Hilbert scheme of points. For the moduli of stable sheaves on a K3 surface with the Picard rank 1, I studied weak Brill-Noether property. This is a joint work with Izzet Coskun and Howard Nuer. For the derived category of an abelian surface, I calculated the categorical entropy of some endofunctor. In particular I confirmed a conjecture of Kikuta and Takahashi in this case.I also studied the birational automorphism group of a generalized Kummer variety.
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| Free Research Field |
代数幾何
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| Academic Significance and Societal Importance of the Research Achievements |
安定層やそのモジュライは微分幾何やYang-Mills理論（インスタントン）と関係し、様々な立場から研究がなされてきた。特に標準束が自明あるいはそれに近い場合、モジュライ空間の標準束も自明あるいはそれに近くなり代数幾何学的に興味深い構造を持っている。この研究ではEnriques曲面や楕円曲面上のモジュライについての双有理同型類、genericな安定層のコホモロジー群の挙動、圏論的エントロピーなどについて成果を得ることができた。
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