Research on CR-approach to the moduli space of toric singularities

本文将强伪凸CR结构的变形理论应用于复解析空间的正规孤立奇点的模空间，是研究孤立奇点变形的一种新方法，而不是标准的代数几何方法。本研究的主要目的是描述一个详细的结构的模空间的正常孤立奇异芽的变形边界CR结构。本文给出了典型循环商曲面奇点的Artin变形的CR描述，并从CR的角度描述了孤立奇点的一些相关变形现象。关于规则部分的模量，找到了复杂结构变形第二障碍消失的一个新条件。

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.