2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/112642Let a finite group $G$ act on the complex plane $({\Bbb C}^2, 0)$. We consider multi-index filtrations on the spaces of germs of holomorphic functions of two variables equivariant with respect to 1-dimensional representations of the group $G$ defined by components of a modification of the complex plane ${\Bbb C}^2$ at the origin or by branches of a $G$-invariant plane curve singularity $(C,0)\subset({\Bbb C}^2,0)$. We give formulae for the Poincare series of these filtrations. In particular, this gives a new method to obtain the Poincare series of analogous filtrations on the rings of germs of functions on quotient surface singularities.Algebraic Geometry14B05; 16W70; 16W22text