| Project/Area Number |
10640013
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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 | NIIGATA UNIVERSITY |
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Principal Investigator |
YOSHIHARA Hisao Faculty of Science, NIIGATA UNIVERSITY Professor, 理学部, 教授 (60114807)
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| Co-Investigator(Kenkyū-buntansha) |
TAJIMA Shin-ichi Faculty of Technology, NIIGATA UNIVERSITY Assistant Professor, 工学部, 助教授 (70155076)
AKIYAMA Shigeki Faculty of Science, NIIGATA UNIVERSITY Assistant Professor, 理学部, 助教授 (60212445)
TAKEUCHI Teruo Faculty of Science, NIIGATA UNIVERSITY Assistant Professor, 理学部, 助教授 (10018848)
TOKUNAGA Hiro-o Kochi University, Faculty of Science, Assistant Professor, 理学部, 助教授 (30211395)
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| Project Period (FY) |
1998 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1999: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1998: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | degree of irrationality / algebraic surface / Kodaira dimension / algebraic curve / Galois point / maximal rational intermediate subfield / 非有理次数 / 極大有理中間体 |
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| Research Abstract |
1. Let Si (I = 1,2) be smooth projective surfaces and f : SィイD21ィエD2 → SィイD22ィエD2 be the surjective morphism. There has been a problem that whether the inequality dr(SィイD21ィエD2) 【greater than or equal】 dr(SィイD22ィエD2) hold true, where dr is the degree of irrationality. We have found examples which do not satisfy the inequality in the class of hyperelliptic surfaces.
2. Let S be a hyperelliptic surface. We have proved that dr(S) = 2, 3 or 4, and that dr(S) = 2 if and only if 2KィイD2sィエD2 is trivial, where KィイD2sィエD2 is the canonical bundle of S.
3. Let C be a plane curve of degree d and K = k(C) be the rational function field of C. We consider a projection пp of C from P ∈ C to a line l =ィイD4〜ィエD4 PィイD11ィエD1. The projection induces the extension of fields πィイD2PィエD2ィイD1*ィエD1 : k(l) * K. We have studied the structure of this extension from geometrical viewpoint. If the extension is Galois, we call P Galois point. We have determined all the Galois points. If P is not a Galois point, we cosider the minimal splitting field Lp of the extension K/k(l) and the Galois group Gal(Lp/k(l)). Our study have been done in this latter case only for d = 4, the general case must be studied in the furture.
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