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May 2008 $C^{l}-\mathcal{G}_{V}-$ determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties
Hengxing LIU, Dun-mu ZHANG
Hokkaido Math. J. 37(2): 309-329 (May 2008). DOI: 10.14492/hokmj/1253539557

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.

Citation

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Hengxing LIU. Dun-mu ZHANG. "$C^{l}-\mathcal{G}_{V}-$ determinacy of weighted homogeneous function germs on weighted homogeneous analytic varieties." Hokkaido Math. J. 37 (2) 309 - 329, May 2008. https://doi.org/10.14492/hokmj/1253539557

Information

Published: May 2008
First available in Project Euclid: 21 September 2009

zbMATH: 1154.58021
MathSciNet: MR2415903
Digital Object Identifier: 10.14492/hokmj/1253539557

Subjects:
Primary: 58A35

Rights: Copyright © 2008 Hokkaido University, Department of Mathematics

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Vol.37 • No. 2 • May 2008
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