Topology of smoothings of non-isolated singularities of complex surfaces

TL;DR

This paper proves that the boundaries of Milnor fibers for smoothings of non-isolated complex surface singularities are graph manifolds and introduces a method to compute their plumbing graphs.

Contribution

It establishes the topological nature of Milnor fiber boundaries and provides a new computational method for associated plumbing graphs.

Findings

Boundaries are graph manifolds

Method to compute plumbing graphs

Enhanced understanding of singularity smoothings

Abstract

We prove that the boundaries of the Milnor fibers of smoothings of non-isolated reduced complex surface singularities are graph manifolds. Moreover, we give a method, inspired by previous work of N\'emethi and Szilard, to compute associated plumbing graphs.