2016 Fiscal Year Final Research Report
A study of complex surface singularities with rational homology sphere link
| Project/Area Number |
26400064
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Yamagata University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
TOMARU TADASHI 群馬大学, 名誉教授 (70132579)
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| Research Collaborator |
Nemethi Andras
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 2次元特異点 / 幾何種数 |
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| Outline of Final Research Achievements |
Giving an explicit topological type of a normal surface singularity with homology sphere link, we determined the all possible values of the geometric genus, the multiplicity, and the embedding dimension, and also obtained the complex structures with maximal geometric genus (joint work with Professor A. Nemethi). For general surface singularities, we gave several characterizations of pg-ideals and an explicit expression for the core of pg-ideals, and proved the existence of good ideals and a new characterization of rational surface singularities via core (joint work with Professor Kei-ichi Watanabe and Professor Ken-ichi Yoshida). We also determined the all possible dimension of cohomology of ideal sheaves given by cycles for elliptic singularities.
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| Free Research Field |
複素特異点論
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