The research of 2-dimensional complex singularities associated to degenerations of closed Riemann surfaces
| Project/Area Number |
16540052
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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 |
Geometry
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| Research Institution | Gunma University |
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Principal Investigator |
TOMARU Tadashi GUNMA UNIVERSITY, Faculty of Medicine, Professor, 医学部, 教授 (70132579)
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| Co-Investigator(Kenkyū-buntansha) |
OKUMA Tomohiro GUNMA UNIVERSITY, Faculty of Education, Art and Science, Assistany Professor, 教育文化学部, 助教授 (00300533)
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| Project Period (FY) |
2004 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2005: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
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| Keywords | singularity / degeneration of Riemann surfaces / pencil genus / singularity with C^*-action / degeneration with C^*-action / rational triple point / Kodaira singularity / 閉Riemann面 / 閉Riemann面の退化族 / 複素乗法群 / 局所モノドロミー群 / Milnorモノドロミー群 |
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| Research Abstract |
In this research, we investigated the following and obtained following results.
(1) We have been investigated the structure of degenerations of closed Riemann surfaces with C^*-action. Four years ago, Tomaru proved that there is a very natural construction of degenerations of closed Riemann surfaces from complex surface singularities and holomorphic functions on the singularities. We prove similar result for normal surface singularities with C^*-action.
(2) Let (X,o) be a normal surface singularity obtained by the contraction of the zero-section of a line bundle on a curve. We gave a necessary and sufficient condition for (X,o) to be Kodaira (or Kulikov) singularity. Using this, we gave an example which is a Kodaira singularity but not a Kulikov singularity.
(3) We determined the value of pencil genus of rational triple points by using Artin's classification of rational triple points and Kodaira's classification of elliptic degenerations.
(4) We prove some results on some relation between quasi-rational singularities and cyclic coverings.
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Report
(3 results)
Research Products
(10 results)
