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

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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.