| Project/Area Number |
13640029
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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 The University of Tokushima, 総合科学部, 教授 (10211111)
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| Co-Investigator(Kenkyū-buntansha) |
HOMMA Masaaki The University of Tokushima, 工学部, 教授 (80145523)
KATO Takao The University of Tokushima, 理学部, 教授 (10016157)
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| Project Period (FY) |
2001 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2002: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2001: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Algebraic Curve / Brill-Noether Theory / special linear system / Brill-Nother理論 |
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| Research Abstract |
Let C be a smooth algebraic curve. Assume that C does not admit a double covering to another curve when C is an eve-gonal curve. We proved that if the dimension of a family of line bundles with degree d in which d is less than g-5, is more than d-3r-2, then C is a d-gonal curve with d【less than or equal】6, a 4-sheeted covering of an elliptic curve or a plane curve of degree 8. This is our first result. Next, in case 6-gonal we can prove that except a triple covering of an elliptic curve, the dimension of a family of line bundles with degree d in which d is less than g-5, should be less than d-3r-3, and in case 4-sheeted covering of an elliptic curve, the same conclusion holds.
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