Multiplier ideals of plane curve singularities via Newton polygons

TL;DR

This paper introduces an effective method to compute multiplier ideals and jumping numbers for plane curve singularities using Newton polygons, extending previous results to broader classes of singularities.

Contribution

It generalizes Howald's theorem by characterizing multiplier ideals via Newton polygons for a wider range of curve singularities, employing toroidal resolutions and valuation sequences.

Findings

Provides an explicit method for computing multiplier ideals

Extends the characterization to certain higher-dimensional singularities

Connects Newton polygons with algebraic invariants of singularities

Abstract

We give an effective method to determine the multiplier ideals and jumping numbers associated with a curve singularity $C$ in a smooth surface. We characterize the multiplier ideals in terms of certain Newton polygons, generalizing a theorem of Howald, which holds when $C$ is Newton non-degenerate with respect to some local coordinate system. The method uses toroidal embedded resolutions and generating sequences of families of valuations, and can be extended to some classes of higher dimensional hypersurface singularities.