A study of complex surface singularities whose link is a rational homology sphere

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We studied fundamental analytic invariants of complex normal surface singularities, such as geometric genus. For a weighted homogeneous singularity with rational homology sphere link, we expressed the dimension of the first cohomology group of the tangent sheaf on the minimal good resolution using Seifert invariants (joint work with A. Nemethi). We introduced a notion of pg-cycle and investigated fundamental properties, and then for Gorenstein singularities and rational singularities, we proved that the good ideal exists, and furthermore that good ideals for rational singularities correspond to nef cycles on the minimal resolution (joint work with Kei-ichi Watanabe and Ken-ichi Yoshida). We also gave an explicit expression of the maximal ideal cycle on a complete intersection of Brieskorn type (joint work with Fan-Ning Meng). This generalizes the results by Konno and Nagashima for Brieskorn hypersurfaces.