## Hokkaido Mathematical Journal

### $C^{l}-\mathcal{G}_{V}-$ determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties

#### Abstract

We provide estimates on the degree of $C^{l}-\mathcal{G}_{V}$-determinacy ($\mathcal{G}$ is one of Mather's groups $\mathcal{R}$ or $\mathcal{K}$) of weighted homogeneous function germs which are defined on weighted homogeneous analytic variety $V$ and satisfies a convenient Lojasiewicz condition. The result gives an explicit order such that the $C^{l}$-geometrical structure of a weighted homogeneous polynomial function germ is preserved after higher order perturbations, which generalize the result on $C^{l}-\mathcal{K}$-determinacy of weighted homogeneous functions germs given by M. A. S. Ruas.

#### Article information

Source
Hokkaido Math. J., Volume 37, Number 2 (2008), 309-329.

Dates
First available in Project Euclid: 21 September 2009

https://projecteuclid.org/euclid.hokmj/1253539557

Digital Object Identifier
doi:10.14492/hokmj/1253539557

Mathematical Reviews number (MathSciNet)
MR2415903

Zentralblatt MATH identifier
1154.58021

Subjects
LIU, Hengxing; ZHANG, Dun-mu. $C^{l}-\mathcal{G}_{V}-$ determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties. Hokkaido Math. J. 37 (2008), no. 2, 309--329. doi:10.14492/hokmj/1253539557. https://projecteuclid.org/euclid.hokmj/1253539557