On Poincare series of filtrations on equivariant functions of two variablesстатья
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Дата последнего поиска статьи во внешних источниках: 29 мая 2015 г.
Аннотация:Let a finite group $G$ act on the complex plane $(C^2,0)$. 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 the exceptional divisor of a modification of the complex plane $C^2$ at the origin or by branches of a $G$-invariant plane curve singularity $(C,0)⊂(C^2,0)$. We give formulae for the Poincaré series of these filtrations. In particular, this gives a new method to obtain the Poincaré series of analogous filtrations on the rings of germs of functions on quotient surface singularities.