# The boundary of the Milnor fiber of the singularity f(x,y) + zg(x,y) = 0

## TL;DR

This paper provides an explicit algorithm to construct the plumbing graph of the boundary of the Milnor fiber for a specific class of complex surface singularities, using common resolutions of the defining functions.

## Contribution

It introduces a novel algorithm that explicitly constructs the plumbing graph for the Milnor fiber boundary based on common resolutions of the functions defining the singularity.

## Key findings

- Provides an explicit plumbing graph construction method.
- Connects resolution data to Milnor fiber boundary topology.
- Enhances understanding of singularity boundaries in complex surfaces.

## Abstract

Let $f,g\in\mathbb{C}\{x,y\}$ be germs of functions defining plane curve singularities without common components in $(\mathbb{C}^2,0)$ and let $\Phi(x,y,z) = f(x,y) + zg(x,y)$. We give an explicit algorithm producing a plumbing graph for the boundary of the Milnor fiber of $\Phi$ in terms of a common resolution for $f$ and $g$.