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For a complete intersection surface singularity of Brieskorn type, we give concrete descriptions of the maximal ideal cycle and the fundamental cycle on the minimal good resolution space. Then we provide a condition for these cycles to coincide, and a condition for the singularity to be a Kodaira singularity. The results are a natural extension of the hypersurface case obtained by Konno and Nagashima.

THE MAXIMAL IDEAL CYCLES OVER COMPLETE INTERSECTION SURFACE SINGULARITIES OF BRIESKORN TYPE