On Poincare series of filtrations on equivariant functions of two variables

Details On Poincare series of filtrations on equivariant functions of two variables On Poincare series of filtrations on equivariant functions of two variables

2006-05-03

arxiv.org/abs/math/0605087v1

Mathematics

Algebraic Geometry

Scientific paper

Let 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.

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