2001 Fiscal Year Final Research Report Summary
Complex analytic research on purely elliptis singularities
| Project/Area Number |
12640202
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
WATANABE Kimio University of Tsukuba, Institute of Mathematics, professor, 数学系, 教授 (50015913)
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| 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)
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| Project Period (FY) |
2000 – 2001
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| Keywords | normal singularity / purely elliptic singularity / plurigenera |
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| 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.
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