| Project/Area Number |
09440005
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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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 | Saitama University |
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Principal Investigator |
SAKAI Fumio Saitama University, Dept. of Math., Professor, 理学部, 教授 (40036596)
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| Co-Investigator(Kenkyū-buntansha) |
FUKUI Toshizumi Saitama University, Dept. of Math., Associate Professor, 理学部, 助教授 (90218892)
YANO Tamaki Saitama University, Dept. of Math., Professor, 理学部, 教授 (10111410)
TAKAUCHI Kisao Saitama University, Dept. of Math., Professor, 理学部, 教授 (00011560)
EBIHARA Madoka Saitama University, Dept. of Math., Lecturer, 理学部, 講師 (80213578)
SATOH Takakazu Saitama University, Dept. of Math., Associate Professor, 理学部, 助教授 (70215797)
SAKAMOTO Kunio Saitama University, Dept. of Math., Professor (70089829)
GON Yasuro Saitama University, Dept. of Math., Assistant (30302508)
OKUMURA Masafumi Saitama University, Dept. of Math., Professor (60016053)
NAGASE Masayoshi Saitama University, Dept. of Math., Professor (30175509)
ARAI Michio Saitama University, Dept. of Math., Assistant (40008850)
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| Project Period (FY) |
1997 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| Budget Amount *help |
¥11,300,000 (Direct Cost: ¥11,300,000)
Fiscal Year 2000: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1999: ¥2,400,000 (Direct Cost: ¥2,400,000)
Fiscal Year 1998: ¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1997: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | plane curve / rational curve / cuspidal curve / multiplicity sequence / quadratic transformation / place at infinity / projective equivalence / maximal multiplicity / 有理関数 / 特異点解消 / 重複度 / 代数曲面 / 変形 / 有理尖点曲線 / 巡回被覆 / 特異点 |
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| Research Abstract |
The head investigator proved that for rational cuspidal plane curves of degree d, the degree d is less than or equal to the 3× the maximal multiplicity (Math.Ann. 285, (1989), 233-247). In the project, if the maximal multiplicity is equal to d-2, rational cuspidal plane curves are completely classified and the defining equations of the curves are determined (Osaka J.Math., 37, (2000), 405-415). As a corollary, it turns out that such rational cuspidal plane curves are transformable into a line by Cremona transformations. The systematic study of the effect of degenerate quadratic transformations on germs of plane curve singularities are used.
The head investigator published a book on algebra (The theory of Rings and Fileds, Kyoritsu, 1997). Based on new concept, the theory of rings and fields are written to the study of algebraic geometry.
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