| Project/Area Number |
16340019
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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 |
Geometry
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| Research Institution | Tokyo University of Science (2005-2006)
Tokyo Metropolitan University (2004) |
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Principal Investigator |
OKA Mutsuo Tokyo University of Science, 理学部, 教授 (40011697)
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| Co-Investigator(Kenkyū-buntansha) |
TERAO Hiroaki Hokkaido University, 理学研究科, 教授 (90119058)
TOKUNAGA Hiroo Tokyo Metropolitan University, 都市教養部理工系, 教授 (30211395)
YOKOTA Yosiyuki Tokyo Metropolitan University, 都市教養部理工系, 助教授 (40240197)
IMAI Jun Tokyo Metropolitan University, 都市教養部理工系, 助教授 (70221132)
SHIMADA Ichiro Hokkaido University, 理学研究科, 助教授 (10235616)
諏訪 立雄 新潟大学, 工学部, 教授 (40109418)
真田 克典 東京理科大学, 理学部, 教授 (50196292)
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| Project Period (FY) |
2004 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥6,600,000 (Direct Cost: ¥6,600,000)
Fiscal Year 2006: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2005: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2004: ¥2,400,000 (Direct Cost: ¥2,400,000)
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| Keywords | Fundamental group / Alexander polynomial / Zariski pairs / theta-Alexander polynomials / Dihedral covers / non-reduced degenerations / tangential Alexander多項式 / non-reduced degeneration / 交点数 / ザリスキー対 / ヤコビアン予想 / 接アレクサンダー多項式 / thetaアレクサンダー多項 / line-退化 / ミルナー束 / トーラス型 |
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| Research Abstract |
We did a systematic research on the singularity theory of plane curves, Fundamental groups of the Complements, Zariski Pairs, Alexander polynomials and its generalization, theta-Alexander polynomials.
This generalization plays an important role for the research of non-reduced degenerations of plane curves and Their fundamental groups.
Tokunaga did a fundamentak research on dihedral covering over plane curves of degree 6 and Zariski pairs.
Shimada did the research of fundamental groups over positive characteristic.
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