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2003 Fiscal Year Final Research Report Summary

Geometry of branched Galois covers and number theory

Research Project

Project/Area Number 14340015
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionTokyo Metropolitan University

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)

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)
Project Period (FY) 2002 – 2003
KeywordsGalois cover / versal cover / fundahnental group / cubic fields / Zariski κ-plet / super singular K3 surfaces / rational double points / Mordell curves
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.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] H.Tokunaga: "Note on a 2-dimensional versal D_8-cover"Osaka Math.J.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] E.Artal Bartolo, H.Tokunaga: "Zariski k-plets of rational curve arrangements and dihedral covers"Topology and its Applications. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Oka: "Alexander polynomial of sextics"Journal of Knot Theory and its ramification. 12. 619-636 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] K.Miyake: "Some Families of Mordell Curves associated to Cubic Fields"Computational and Applied Math.. 160. 217-231 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] I.Shimada: "Rational double points on supersingular K3 surfaces"Math.Comp.. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Nakamura, H.Tsunogai: "Harmonic and equianharmonic equations in the Grothendieck-Teich-muller group"Forum Mathematicum. 15. 877-892 (2003)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Tokunaga: "Note no a 2-dimensional versal D_8-cover"Osaka Math.J.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] E.Artal Bartolo, H.Tokunaga: "Zariski κ-plets of rational curve arrangements and dihedral covers"Topology and its Applications. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M.Oka: "Alexander polynomial of sextics"Journal of Knot Theory and its ramification. 12. 619-636 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] K.Miyake: "Some Families of Mordell Curves associated to Cubic Fields"Computational and Applied Math.. 160. 217-231 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] I.Shimada: "Rational double points on supersingular K3 surfaces"Math.Comp.. (in press).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H.Nakamura, H.Tsunogai: "Harmonic and equianharmonic equations in the Grothendieck-Teichmuller group"Form Mathematicum. 15. 877-892 (2003)

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2005-04-19  

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