Motivic local density of isolated surface singularities

TL;DR

This paper computes the motivic local density of isolated algebraic surface singularities to relate it with algebraic multiplicity, incorporating inner rate data from bilipschitz geometry.

Contribution

It introduces a method to connect motivic local density with algebraic multiplicity using bilipschitz geometric data.

Findings

Motivic local density can be explicitly computed for isolated surface singularities.

Inner rate data influences the motivic local density calculation.

The link between motivic density and algebraic multiplicity is clarified.

Abstract

The goal of this paper is to compute the motivic local density of an isolated algebraic surface singularity, in order to explain its link with algebraic multiplicity. In this context, we can use an additional data: the inner rate related to the bilipschitz geoemtry of the singularity, as studied by A. Belotto da Silva, L. Fantini and A. Pichon.