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Bibliographic Record
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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 CR-approach to the moduli space of toric singularities
- Text Language Code
- jpn
- Target Audience
- 一般
- Note (General)
- 2011-2013年度科学研究費助成事業（基盤研究（C））研究成果報告書 課題番号：23540099 研究代表者：宮嶋公夫（鹿児島大学・理工学研究科・教授）本研究は、境界CR構造の変形を通じて正規孤立特異点の変形へアプローチするという従来とは異なる視点に基づく研究の一環として行われ、特異点の個別性に基づいた詳細なモジュライ空間の把握を目的とした。特に、トーリック特異点の代表例である2次元巡回商特異点の変形を中心として研究を行い、典型的なArtin変形族のCR表示とそれに基づく特異点の変形の記述を行った。また、非特異部分のモジュライに関連して、複素構造の変形の2次障害の新しい消滅方向が見出された。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.