# Motivic Milnor fibers of plane curve singularities

## TL;DR

This paper presents a combinatorial method to compute motivic Milnor fibers of plane curve singularities using resolution graphs, enabling analysis of their Hodge-Steenbrink spectrum through quasi-homogeneous singularities.

## Contribution

Introduces an inductive, combinatorial approach to compute motivic Milnor fibers using extended simplified resolution graphs, linking to Hodge-Steenbrink spectrum analysis.

## Key findings

- Method allows computation of motivic Milnor fibers for plane curve singularities.
- Connects the spectrum of such singularities to that of quasi-homogeneous ones.
- Facilitates spectral study via combinatorial resolution data.

## Abstract

We compute the motivic Milnor fiber of a complex plane curve singularity in an inductive and combinatoric way using the extended simplified resolution graph. The method introduced in this article has a consequence that one can study the Hodge-Steenbrink spectrum of such a singularity in terms of that of a quasi-homogeneous singularity.