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Complex analytic research on purely elliptis singularities

Research Project

Project/Area Number 12640202
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

WATANABE Kimio  University of Tsukuba, Institute of Mathematics, professor, 数学系, 教授 (50015913)

Co-Investigator(Kenkyū-buntansha) MASUDA Tetusya  University of Tsukuba, Institute of Mathematics, associate professor, 数学系, 助教授 (70202314)
SAKAI Tateaki  University of Tsukuba, Institute of Mathematics, professor, 数学系, 教授 (80087436)
KIMURA Tatsuo  University of Tsukuba, Institute of Mathematics, professor, 数学系, 教授 (30022726)
Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Keywordsnormal singularity / purely elliptic singularity / plurigenera / 単純楕円型特異点 / カスプ特異点 / 変形族 / 複素解析 / 超曲面 / 孤立特異点
Research Abstract

Let (X, x) be a purely elliptic singularity, I.e., the plurigenera δ_m(X, x) of the singularity (X, x) is equalto 1 for every m [0x81b8(Shift-JIS)] N. In the two dimensional case, simple elliptic singularities and cusp singularities are purely elliptic singularities.
On the other hand, Knoller defined other plurigenera {γ_m(X, x)}_<mN> for a normal isolated singularity (X,x), Between δ_m(X,x) and γ_m(X,x) there is an inequality 0 【less than or equal】 δ_m(X,x) 【less than or equal】 γ_m(X,x).
Then the plurigenera γ_m(X, x) make it possible for us to classify purely elliptic singularities.
We describe some properties of Knoller's plurigenera defined for normal isolated singularities, especially in case singularities are so-called hypersurfce purely elliptic singularities.
Consequently we have made examples of families for hypersurfce purely elliptic sungularities with constant γ_m.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (3 results)

All Other

All Publications (3 results)

  • [Publications] Naohiro Kanesaka and Kimio Watanabe: "On plurigenera of hyper surface purely elliptic singulariyies"Kumamoto J. Math.. 21-37 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] N.Kanesaka, K.Watanabe: "On plurigenera of hypersurface purely elliptic singularities"Kumamoto J. Math.. Vol.13. 21-37 (2000)

    • Related Report
      2001 Annual Research Report
  • [Publications] N.Kanesaka: "On plurigenera of hypersurface purely elliptic singularities"Kumamoto Journal of Mathematics. Vol.13. 21-37 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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