2003 Fiscal Year Final Research Report Summary
Geometry of branched Galois covers and number theory
| Project/Area Number |
14340015
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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 | Tokyo Metropolitan University |
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Principal Investigator |
TOKUNAGA Hiroo Tokyo Metropolitan University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30211395)
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| Co-Investigator(Kenkyū-buntansha) |
SHIMADA Ichiro Hokkaido University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (10235616)
MIYAKE Katsuya Tokyo Metropolitan University, Graduate School of Science, Associate Professor, 大学院・理学研究科, 教授 (20023632)
OKA Mutsuo Tokyo Metropolitan University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40011697)
TSUCHIHASHI Hiroyasu Tohoku Gakuin University, Department of Liberal Arts, Associate Professor, 教養学部, 助教授 (00146119)
NAKAMURA Hiroaki Okayama University, Faculty of Science, Professor, 理学部, 教授 (60217883)
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| Project Period (FY) |
2002 – 2003
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| Keywords | Galois cover / versal cover / fundahnental group / cubic fields / Zariski κ-plet / super singular K3 surfaces / rational double points / Mordell curves |
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| Research Abstract |
1.Construction problem of branched Galois covers and the inverse Galois problem : This project were manly carried out by Tokunaga, Miyake and Tsuchihashi. Tokunaga mainly studied on 2-dimensional versal Galois covers. Two papers on 2-dimensional versal Galois covers and rational elliptic surfaces are in press. Also he show that the study on 2-dimensional versal Galois covers is reduced to that of Cremona representations of finite groups. The paper on this subject is now in preparation. Tsuchihashi constructed versal Galois covers for dihedral groups and the symmetric group by using toric geometry. He also studied Galois covers of P^2 whose universal cover is polydisc. Miyake introduced two ellitpic curves defined over Q, which is related to certain cubic fields, and gave explicit short forms so-called "Mordell Cures."
2.Topology of open algebraic varieties and singularities : Nakamura made investigation on Grothendieck-Teichmuller group. Tokunaga made study on Zariski κ-plets with Artal Bartolo of Universidad Zaragoza, and gave a new example. This result is in press. Oka intesively studied plane sextic cures. Shimada classified all possible configurations of rational double points on super singular K3 surfaces with Picard number 21.
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