Motivic local density of isolated surface singularities

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.