Normal reduction numbers of normal surface singularities

TL;DR

This paper surveys the concept of normal reduction numbers in normal surface singularities and introduces new results on their invariants for Brieskorn complete intersections.

Contribution

It provides a comprehensive survey and presents novel findings on the normal reduction numbers of Brieskorn complete intersections.

Findings

Results on elliptic and cone-like singularities

New invariants for Brieskorn complete intersections

Enhanced understanding of normal reduction numbers

Abstract

This article consists of two parts. The first part is a survey on the normal reduction numbers of normal surface singularities. It includes results on elliptic singularities, cone-like singularities and homogeneous hypersurface singularities. In the second part, we prove a new results on the normal reduction numbers and related invariants of Brieskorn complete intersections.