Weighted homogeneous surface singularities homeomorphic to Brieskorn complete intersections

TL;DR

This paper investigates weighted homogeneous surface singularities, specifically those homeomorphic to Brieskorn complete intersections, focusing on maximizing geometric genus and conditions for the maximal ideal cycle to match the fundamental cycle.

Contribution

It provides new insights into the geometric genus maximization and ideal cycle conditions for these specific surface singularities.

Findings

Characterization of conditions for maximal geometric genus

Identification of when the maximal ideal cycle equals the fundamental cycle

Analysis of weighted homogeneous singularities related to Brieskorn 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.