2019 Fiscal Year Final Research Report
Study on algebraic surfaces via fibration structure
| Project/Area Number |
15K04825
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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 | Kagoshima University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
松村 慎一 東北大学, 理学研究科, 准教授 (90647041)
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Keywords | 一般型代数曲面 |
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| Outline of Final Research Achievements |
The purpose of this study was developing some approach for the study of fibration structures, and its application to some problems on complex algebraic surfaces of general type. In addition to some partial results on the original purposes, we obtained as their application some results on minimal complex surfaces with the first Chern number 9, the Euler characteristic of the structure sheaf 5, and the first Chern class divisible by 3. These include a complete structure theorem for the surfaces of this class, the uniqueness of the underlying differentiable structure, the unirationality and the dimension of the moduli space, and some concrete descriptions on the behaviour of the canonical map.
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| Free Research Field |
複素代数幾何学
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| Academic Significance and Societal Importance of the Research Achievements |
上に述べた我々の曲面は幾何種数が 4 になるが，幾何種数 4 の一般型曲面は，標準写像の振る舞いの観点から，古くから注目されてきたクラスであり，現在ほとんど分かっていない第 1 Chern 数が 8 以上の場合に，モジュライ空間の連結成分をまるまる 1 つ見つけ，研究を押し進めることができた．代数曲線束構造の今後の研究についての手がかりの為のものであったが，2-標準写像の非双有理性の研究についての副産物的な小結果に繋がったほか，今野一宏氏による正規標準曲面の研究とも関連が判明した．
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