A recursive formula for the motivic Milnor fiber of a plane curve

TL;DR

This paper introduces a recursive formula for the motivic Milnor fiber of an irreducible plane curve, utilizing truncation and derived curves, and extends it to the Hodge-theoretic spectrum.

Contribution

It presents a novel recursive approach for computing motivic Milnor fibers and their Hodge spectra for plane curves, advancing understanding in algebraic geometry.

Findings

Derived a recursive formula for motivic Milnor fibers

Extended recursion to Hodge-theoretic spectrum

Provides computational tools for plane curve invariants

Abstract

We find a recursive formula for the motivic Milnor fiber of an irreducible plane curve, using the notions of a truncation and derived curve. We then apply natural transformations to obtain a similar recursion for the Hodge-theoretic spectrum.