Leonardo Meireles Câmara

arXiv2020

On the moduli space of quasi-homogeneous functions

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-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.

math.CV↗

arXiv2010

On the classification of quasi-homogeneous curves

We apply techniques of Holomorphic Foliations in the description of the analytic invariants associated to germs of quasi-homogeneous curves in $(\mathbb{C}^2,0)$. As a consequence we obtain an effective method to determine whether two quasi-homogeneous curves are analytically equivalent.

math.AG↗