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 (but not homogeneous) functions with constant Henry–Parusiński 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–Parusiński invariant providing a maximum quota for this number. Finally, we conclude that the moduli space of bi-Lipschitz equivalent quasi-homogeneous function-germs admits an analytic structure.
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M.A.S. Ruas was partially supported by FAPESP Proc. 2019/21181-0 and CNPq Proc. 305695/2019-3.
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Câmara, L.M., Ruas, M.A.S. On the Moduli Space of Quasi-Homogeneous Functions. Bull Braz Math Soc, New Series 53, 895–908 (2022). https://doi.org/10.1007/s00574-022-00287-8
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DOI: https://doi.org/10.1007/s00574-022-00287-8