Séminaire de géométrie du 25 novembre 2026 à 14h - salle de conférences du CMLS

Titre : Motivic local density of isolated singularities of algebraic varieties

 

Résumé : We consider $K$ a field equipped with a distance and a measure. The local density of a set $X$ in $K^n$ at a point is defined as the limit, if it exists, of normalized local volumes. This notion can be generalized to fields for which there is no classical measure theory, as $\mathbb{C}((t))$, using motivic integration. The goal of this talk is to present a formula computing the motivic local density of isolated singularities of algebraic varieties. In the special case of surfaces, we can use an additional data: the inner rates related to the bilipschitz geometry of the singularity, introduced by Birbair, Neumann and Pichon. In the general case, we prove that the motivic local density can be computed as the residue in 1 of a Zeta function defined with normalized local volumes.