2013 Fiscal Year Final Research Report
Research on CR-approach to the moduli space of toric singularities
| Project/Area Number |
23540099
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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 | Kagoshima University |
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Principal Investigator |
MIYAJIMA Kimio 鹿児島大学, 理工学研究科, 教授 (40107850)
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| Co-Investigator(Kenkyū-buntansha) |
YOKURA Shoji 鹿児島大学, 大学院・理工学研究科, 教授 (60182680)
AIKOU Tadashi 鹿児島大学, 大学院・理工学研究科, 教授 (00192831)
OBITSU Kunio 鹿児島大学, 大学院・理工学研究科, 准教授 (00325763)
AKAHORI Takao 兵庫県立大学, 大学院・物質理学研究科, 教授 (40117560)
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| Project Period (FY) |
2011 – 2013
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| Keywords | CR構造 / 特異点 / 複素解析幾何 |
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| Research Abstract |
This research is an application of the deformation theory of strongly pseudo-convex CR structures to the moduli space of normal isolated singularities of complex analytic spaces, that is a new approach rather than a standard algebro-geometric approach to deformation of isolated singularities. The main purpose of this research is to describe a detailed structure of the moduli space of normal isolated singularity germs in terms of deformation of boundary CR structures. In this research, CR description of the Artin deformation of typical cyclic quotient surface singularities are obtained and some related deformation phenomena of isolated singularities are also described from the CR viewpoint. Concerning the moduli of the regular part, a new condition for the vanishing of the second obstruction of deformation of complex structure is found.
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Research Products
(10 results)
