A comprehensive approach to the moduli space of quasi-homogeneous singularities (1407.4554v1)

Published 17 Jul 2014 in math.CV

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

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