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This article is cited in 10 scientific papers (total in 10 papers)
On Poincaré series of filtrations on equivariant functions of two variables
A. Campilloa, F. Delgadoa, S. M. Gusein-Zadeb a University of Valladolid
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
Let a finite group $G$ act on the complex plane $(\mathbb C^2,0)$. 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 $\mathbb C^2$ at the origin or by branches of a $G$-invariant plane curve singularity $(C,0)\subset(\mathbb C^2,0)$. 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.
Key words and phrases:
Equivariant functions, filtrations, Poincaré series.
Received: May 24, 2006
Citation:
A. Campillo, F. Delgado, S. M. Gusein-Zade, “On Poincaré series of filtrations on equivariant functions of two variables”, Mosc. Math. J., 7:2 (2007), 243–255
Linking options:
https://www.mathnet.ru/eng/mmj281 https://www.mathnet.ru/eng/mmj/v7/i2/p243
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Abstract page: | 325 | References: | 68 |
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