Research of Quasi-Kodaira singularities

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In this research, we have investigated the relation between degeneration of algeraic curves and normal surface singularities. First we gave the definiton of quasi-Kodaira singularities and gave some sufficient conditions for normal surface singularities to be quasi-Kodaira. Second we considered hypersuface normal surface singularities (namely, the equation is z^n=f(x,Y) ). For the class, we found an interesting class of quasi-Kodaira singularities. Third, we prove an interesting result about cyclic covers of normal surface singularities. Under some conditions, if the order of the group of the cyclic cover is sufficiently large, then the cyclic cover over a normal surface singularity is a quasi-Kodaira singularity. Fourth, we prove some formulae about geometric genus of elliptic quasi-Kodaira singularity.