2010 Fiscal Year Final Research Report
Research on the moduli of the geometric structure on a boundary of isolated singularities
| Project/Area Number |
20540087
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Geometry
|
|---|
| Research Institution | Kagoshima University |
|---|
Principal Investigator |
MIYAJIMA Kimio Kagoshima University, 理工学研究科(理学系), 教授 (40107850)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YOKURA Shoji 鹿児島大学, 理工学研究科(理学系), 教授 (60182680)
AIKOU Tadashi 鹿児島大学, 理工学研究科(理学系), 教授 (00192831)
OBITSU Kunio 鹿児島大学, 理工学研究科(理学系), 准教授 (00325763)
ITOH Minoru 鹿児島大学, 理工学研究科(理学系), 准教授 (60381141)
AKAHORI Takao 兵庫県立大学, 大学院・物質理学研究科, 教授 (40117560)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
ITOH Mitsuhiro 筑波大学, 大学院・数理物質科学研究科, 名誉教授 (40015912)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Keywords | 複素解析幾何学 / CR構造 / 特異点 / モジュライ / 変形 |
|---|
| Research Abstract |
The following three results are obtained about the boundary description on the moduli of normal isolated complex singularities :
(1) Descriptions of the first order deformations of rational surface singularities A_<n,q> are obtained using the invariant spherical harmonic forms.
(2) The versal deformation of resolution of normal isolated singularities is complex analytically constructed.
(3) A framework of constructing the versal deformation of CR structures with fixing a contact structures on a boundary of normal isolated singularities of complex dimension three or higher is established under the equivalence of CR structures connected by the Hamiltonian flows.
|
