We study the relationship between singular holomorphic foliations in$(\mathbb{C}^{2},0)$ and their separatrices. Under mild conditions we describea complete set of analytic invariants characterizing foliations withquasi-homogeneous separatrices. Further, we give the full moduli space ofquasi-homogeneous plane curves. This paper has an expository character in orderto make it accessible also to non-specialists.
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