On the classification of analytic differential equations in $(\Bbb{C}^{2},0)$

Leonardo Câmara

Keywords: holomorphic foliations | holonomy | resolution of singularities

We study the classification of analytic differential equations in $(\Bbb{C}^{2},0)$. We give a complete set of analytic invariants determining the analytic type of the underling foliation. In particular we generalize some previous results about dicritical singularities in a straightforward manner. Such problem has its origins in a conjecture proposed by R. Thom in the middle 1970s.

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