Linear Systems and Projective Models on Algebraic Curves
| Project/Area Number |
21540043
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | The University of Tokushima |
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Principal Investigator |
OHBUCHI Akira 徳島大学, 大学院・ソシオ・アーツ・アンド・サイエンス研究部, 教授 (10211111)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Takao 山口大学, 理学部, 教授 (10016157)
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| Co-Investigator(Renkei-kenkyūsha) |
KOMEDA Jiryo 神奈川工科大学, 工学部, 教授 (90162065)
HOMMA Masaaki 神奈川大学, 工学部, 教授 (80145523)
YOSHIHARA Hisao 新潟大学, 理学部, 教授 (60114807)
MIURA Kei 宇部工業高等専門学校, 准教授 (50353321)
TAKAHASHI Takeshi 長岡工業高等専門学校, 准教授 (60390431)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 代数幾何 / 代数曲線 / 特殊線形系 / ブリル=ネーター理論 |
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| Research Abstract |
IIt holds s_c(2)≦g+ 2 for any algebraic curve C with genus g where. s_c(2) is the minimal degree of plane models of C. Martens and Keem conjectured that s_c(2)=g-t+ 2holds for an algebraic curve C admitting a double covering to a curve of genus t. In this research, we can conclude that Martens and Keem conjecture is true for t=0, 1 and t=2 with g≧10, however we can find an important counter examples for every g≦9. On 05-06, December, 2009, we held 7th Annual Conference of Algebraic Curves and Related Topics at Yokohama National Universiy, on 11-12, December, 2010, we held 8th Annual Conference of Algebraic Curves and Related Topics at Saitama Universiy and on 10-11, December, 2011, we held 9th Annual Conference of Algebraic Curves and Related Topics at Tokyo Metropolitan Universiy, respectively. We can get some good results about the minimal degree for plane models o f an algebraic curve.
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Report
(4 results)
Research Products
(8 results)
