Multiplier ideals of analytically irreducible plane curves

Abstract

Let S be a Puiseux series of the germ of an analytically irreducible plane curve Z. We provide a new perspective to construct a set of polynomials F = {F1, . . . , Fg−1} associated to S, which is a special choice of maximal contact elements constructed in [AMB17] and approximate roots defined in [Dur18], [AM73a], [AM73b]. Using these polynomials as building blocks, we describe a set of generators of multiplier ideals of the form I(αZ) with 0 < α < 1 a rational number, which recovers the results about irreducible plane curves in [AMB17], [Dur18].

Multiplier ideals of plane curve singularities via Newton polygons

“…In his PhD Thesis, the third named author described the jumping numbers and the generators of the multiplier ideals associated with a plane branch C on a smooth surface in terms of the semi-roots of C by using Newton maps (see [GD18]). Zhang obtained also similar results as Guzmán with different techniques [Zha19]. The fourth author generalized these results to any plane curve singularity by using Eggers-Wall trees and toroidal modifications (see [RB19]).…”