2006 Fiscal Year Final Research Report Summary
Hypersurface singularity theory from fundamental group
| 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)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Fundamental group / Alexander polynomial / Zariski pairs / theta-Alexander polynomials / Dihedral covers / non-reduced degenerations |
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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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