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Research of Quasi-Kodaira singularities

Research Project

Project/Area Number 10640062
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionGunma University

Principal Investigator

TOMARU Tadashi  Faculty of Medicine, Gunma University Professor, 医学部, 教授 (70132579)

Co-Investigator(Kenkyū-buntansha) OKUMA Tomohiro  Gunma Institute of Technology, lecturer, 一般教科, 講師 (00300533)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1999: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1998: ¥500,000 (Direct Cost: ¥500,000)
Keywordssingularity / degeneration / curve / pencil genus / geometric genus / 代数曲線の退化族 / 基本サイクル / 有限巡回被覆 / 基本種数
Research Abstract

In this research, we have investigated the relation between degeneration of algeraic curves and normal surface singularities. First we gave the definiton of quasi-Kodaira singularities and gave some sufficient conditions for normal surface singularities to be quasi-Kodaira. Second we considered hypersuface normal surface singularities (namely, the equation is z^n=f(x,Y) ). For the class, we found an interesting class of quasi-Kodaira singularities. Third, we prove an interesting result about cyclic covers of normal surface singularities. Under some conditions, if the order of the group of the cyclic cover is sufficiently large, then the cyclic cover over a normal surface singularity is a quasi-Kodaira singularity. Fourth, we prove some formulae about geometric genus of elliptic quasi-Kodaira singularity.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] 奥間智弘: "The Polynomiol periodicity of Pluri-generd of surface singularities"Saitama Math. J.. 17. 7-13 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 都丸正: "On Kodaira singularities defined by Z^n=f(x,y)"Mathematische Zeitshnft. (印刷中).

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Okuma: "The polynomial periodicity of pluri-genera of surface singularities"Saitama Math. J.. 17. 7-13 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Tomaru: "On Kodaira singularities defined by ZィイD1nィエD1=f(x,y)"Mathematische Zeitschrift. (in print).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 都丸正: "On Kodaira singularities defined by Z^n=f(x,y)"Mathematische Zeitschrift (1999.10.アクセプト). (予定).

    • Related Report
      1999 Annual Research Report
  • [Publications] 奥間智弘: "The polynomial periodicity of the pluri-genera of surface singularities"Saitama Mathematical Journal. 17(未定). (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 奥間智弘: "The second pluri-genera of surface singularities"Compositio Mathematica. 110. 263-276 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 奥間智弘: "The pluri-genera of surface singularities"Tohoku Mthematical Journal. 94. 119-132 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 都丸 正: "On maximal icleal cycles for 2-dimensional normal double points" 群馬大学医学部保健学科紀要. 18巻. 17-22 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 奥間智弘: "The second plon-qenus of surface sihgularlties" Compositio Math.110. 263-276 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 奥間智弘: "The pluri-genera of surface sihgularties" Tohoku Math. J.50. 115-132 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 奥間智弘: "The polynomial penodiclty of the plun-genera of surface sihgularties" Sartanid Math. J.17(発表予定). (1999)

    • Related Report
      1998 Annual Research Report

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Published: 1998-04-01   Modified: 2016-04-21  

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