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- Material Type
- 文書・図像類
- Author/Editor
- 宮嶋, 公夫
- Author Heading
- Publication, Distribution, etc.
- Alternative Title
- Research on the moduli of the geometric structure on a boundary of isolated singularities
- Text Language Code
- jpn
- Target Audience
- 一般
- Note (General)
- 2008-2010年度科学研究費補助金(基盤研究(C))研究成果報告書 課題番号：20540087 研究代表者：宮嶋公夫 (鹿児島大学大学院理工学研究科（理学系）教授)複素解析空間の正規孤立特異点のモジュライの境界構造による記述に関して，以下の成果を得た．(1) 準斉次特異点の典型である An,q型有理曲面特異点に関して，その１次変形の不変球面調和形式による具体的記述を得た．(2) 正規孤立特異点の特異点解消空間について，その完備変形族の複素解析的構成を行った．(3) 複素３次元以上の正規孤立特異点の完備変形族構成に関して，固定した実接触構造上での ハミルトン流による境界CR構造の同一視という観点での枠組みを構成した．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.