On the moduli space of quasi-homogeneous functions

Autor: Câmara, Leonardo Meireles, Ruas, Maria Aparecida Soares
Rok vydání: 2020
Předmět:
Druh dokumentu: Working Paper
DOI: 10.1007/s00574-022-00287-8
Popis: 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.
Databáze: arXiv
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