Studies of the geography of fibrations of algebraic curves from the theory of higher degree coverings and muduli spaces
| Project/Area Number |
15K04833
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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 | Ube National College of Technology |
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Principal Investigator |
Ishida Hirotaka 宇部工業高等専門学校, 一般科, 教授 (30435458)
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| Co-Investigator(Renkei-kenkyūsha) |
ASHIKAGA Tadashi 東北学院大学, 工学部, 教授 (90125203)
SHIRANE Taketo 宇部工業高等専門学校, 一般科, 准教授 (70615161)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 代数曲面 / 代数曲線束 / 高次被覆 / 曲面特異点 / モジュライ空間 |
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| Outline of Final Research Achievements |
We study the problem of the geography of fibrations of algebraic curves which is the question of which triplets of the relative Euler-Poincare characteristic, the self-intersection number of the relative canonical divisor and the genus of a fiber can occur for surfaces of general type with a fibration over smooth projective algebraic curve. By using the theory of triple coverings and Galois quadruple coverings, we give inequalities among these invariants for fibrations of Clifford index 1 and 2. Also we prove the existence of many fibrations of algebraic curves by newly developed methods for constructing the coverings of the projective line bundles.
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Report
(4 results)
Research Products
(4 results)
