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arXiv · 2004.03778

On the moduli space of quasi-homogeneous functions

Leonardo Meireles Câmara·Maria Aparecida Soares Ruas
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Abstract

We relate the moduli space of analytic equivalent germs of reduced quasi-homogeneous functions at $(\mathbb{C}^2,0)$ with their bi-Lipschitz equivalence classes. We show that any non-degenerate continuous family of (reduced) quasi-homogeneous functions with constant Henry-Parusi\'nski invariant is analytically trivial. Further we show that there are only a finite number of distinct bi-Lipschitz classes among quasi-homogeneous functions with the same Henry-Parusi\'nski invariant providing a maximum quota for this number.

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Leonardo Meireles Câmara, Maria Aparecida Soares Ruas. 2020-04-08. On the moduli space of quasi-homogeneous functions. https://doi.org/10.1007/s00574-022-00287-8

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