| Project/Area Number |
17540030
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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, Faculty of Integrated Arts and Sciences, Professor, 総合科学部, 教授 (10211111)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Takao YamaguchiUniversity, Faculty of Science, Professor, 理学部, 教授 (10016157)
KOMEDA Jiryo Kanagawa Institute of Technology, Department of Mathematics, Professor, 工学部, 教授 (90162065)
KONNO Kazuhiro Osaka University, Faculty of Science, Professor, 大学院・理学研究科, 教授 (10186869)
NAMBA Makoto Ohtemon University, College of Economics, Professor, 経済学部, 教授 (60004462)
HOMMA Masaaki Kanagawa University, Department of Mathematics, Professor, 工学部, 教授 (80145523)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
Fiscal Year 2005: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | Algebraic Curve / Special Linear System / Brill-Nother Theory / BrilI-Nother理論 |
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| Research Abstract |
Let W^r_d (C)
be a scheme of line bundles defined by usually, can be defined as a subscheme of Pic^d (C)). Kempfand Kleiman-Laksov prove that the variety W^r_d (C) hasdimension at least p = g-(r+1)(g-d+r). Griffith -Harris and Fulton-Lazarsfeld prove that W^r_d(C) is smooth of dimension p = g-(r+1)(g-d+r) when C is a general curve in the moduli space M_g. "A general curve" means there is an open subset U⊂M_g in M_g, W^r_d(C) is smooth of dimension p = g-(r+1)(g-d+r) for any curve C ∈ U. For a curve C which admits a double covering π:C→E to a curve E of genus h, i.e. a curve which we can not regard as a general curve, we can expect many interesting structure of W^r_d (C). In the papers, we give many good properties of W^r_d(C), especially W^1_d(C).
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