On Poincare series of filtrations on equivariant functions of two variables

2006/05/03 by Campillo, A., Delgado, F., Gusein-Zade, S. M.
#14B05 #16W22 #16W70 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0605087

Abstract

Let a finite group G act on the complex plane (\Bbb C², 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 C² at the origin or by branches of a G-invariant plane curve singularity (C,0)⊂(\Bbb C²,0). 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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