Research on the moduli of the geometric structure on a boundary of isolated singularities

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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.