Boundary of the Milnor fiber of a Newton non degenerate surface singularity

TL;DR

This paper presents an explicit combinatorial algorithm to describe the Milnor fiber of Newton non-degenerate surface singularities as a graph manifold, extending previous methods for complex surface singularities.

Contribution

It introduces a new combinatorial algorithm specifically for Newton non-degenerate surface singularities, providing a detailed description of their Milnor fiber boundary.

Findings

Algorithm effectively describes Milnor fiber boundary as a graph manifold

Extends previous methods to a broader class of singularities

Provides explicit combinatorial tools for complex surface singularities

Abstract

We give in this work an explicit combinatorial algorithm for the description of the Milnor fiber of a Newton non degenerate surface singularity as a graph manifold. This is based on a previous work by the author describing a general method for the computation of the boundary of the Milnor fiber of any reduced non isolated singularity of complex surface.