Multiplier ideals of plane curve singularities via Newton polygons

Pedro D. González Pérez, Manuel González Villa, Carlos R. Guzmán Durán, Miguel Robredo Buces

Published 2021-09-27, updated 2023-09-07Version 2

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.