Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections

Abstract

For a given topological type of a normal surface singularity, there are various types of complex structures which realize it. We are interested in the following problem: Find the maximum of the geometric genus and a condition for that the maximal ideal cycle coincides with the undamental cycle on the minimal good resolution. In this paper, we study weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersection singularities from the perspective of the problem.

arXiv comment24 pages. Version2: deleted Remark 2.7, added Remark 4.16, improved the last remark, and minor corrections. Version 3: minor changes; Lemma 4.3 and Proposition 4.9 are improved