Complex analytic research on purely elliptis singularities

Research Project

Project/Area Number	12640202
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Single-year Grants
Section	一般
Research Field	Global analysis
Research Institution	University 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)
Keywords	normal 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.