On Poincare series of filtrations on equivariant functions of two variables
On Poincare series of filtrations on equivariant functions of two variables
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关于二变量等变函数的庞加莱级数过滤
DOI：
10.17323/1609-4514-2007-7-2-243-255
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
S. Gusein
中科院分区：
文献类型：
--
作者：
A. Campillo;F. Delgado;S. Gusein
让有限群 $G$ 作用于复平面 $({\Bbb C}^2, 0)$。我们考虑对两个变量的全纯函数的胚芽空间进行多索引过滤，这两个变量相对于群 $G$ 的一维表示来说是等变的，该群 $G$ 是由原点处的复平面 ${\Bbb C}^2$ 的修改分量或 $G$ 不变平面曲线奇点 $(C,0)\subset({\Bbb C}^2,0)$ 的分支定义的。我们给出了这些过滤的庞加莱级数的公式。特别是，这提供了一种新方法来获得商表面奇点上函数萌芽环上的庞加莱级数类似过滤。
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.