Multiplier ideals of plane curve singularities via Newton polygons

Abstract

We give a description of the multiplier ideals and jumping numbers associated with a plane curve singularity in a smooth surface in terms of Newton polygons. Our approach is inspired by a theorem of Howald about multiplier ideals of Newton non-degenerate hypersurfaces and our results provide a generalization of it to the case of plane curve singularities. We use toroidal embedded resolutions, which can be applied to the case of quasi-ordinary hypersurface singularities.

KEYWORDS:

• Jumping numbers
• multiplier ideals
• plane curve singularities
• toroidal resolutions

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 14B05
• 14F18
• 14M25
• 14H20

Acknowledgments

We are grateful to Patrick Popescu-Pampu for his comments on a preliminary version of this paper. We would like to thank the referee for the suggestions which have helped us to improve the presentation of the paper.

Additional information

Funding

The first and second authors are supported by the grant PID2020-114750GB-C32. The third author was supported by CONACYT Postdoctoral grant 2018-000022-01EXTV. The fourth author was supported by SEV-2015-0554.