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2001 Fiscal Year Final Research Report Summary

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
Keywordsnormal singularity / purely elliptic singularity / plurigenera
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.

  • Research Products

    (1 results)

All Other

All Publications (1 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

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Published: 2003-09-17  

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