On divisorial filtrations associated with Newton diagrams

TL;DR

This paper studies divisorial filtrations linked to Newton diagrams in hypersurface singularities, computing their multi-variable Poincaré series, and explores similar concepts for plane curve singularities.

Contribution

It introduces a method to compute multi-variable Poincaré series for divisorial filtrations associated with Newton diagrams and extends the analysis to plane curve singularities.

Findings

Computed multi-variable Poincaré series for Newton diagram-related filtrations

Extended divisorial filtration analysis to plane curve singularities

Provided explicit formulas for Poincaré series in these contexts

Abstract

We consider divisorial filtration on the rings of functions on hypersurface singularities associated with Newton diagrams and their analogues for plane curve singularities. We compute the multi-variable Poincar\'e series for the latter ones.