An Upper Bound of Geometric Genusof Normal Two-Dimensional Singularities

We will define an invariant Lf for a normal two-dimensional singularity defined as a ratio of K′ divided by Z0, where K′(resp.Z0) is the numerical canonical cycle (resp. Artin’s fundamental cycle). Then we can show a simple upper bound of the geometric genus which have a similar style as the inequality by the length of elliptic sequence due to S.S-T. Yau. ((1)ofTheorem1). The Gorensteinness of maximally elliptic singularities is extended into (2) of our Theorem 1.