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arXiv · 2008.00719

Pairs of foliations and Mattei-Moussu's theorem

Adjaratou Arame Diaw·Frank Loray
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Abstract

We prove a reduction of singularities for pairs of foliations by blowing-up, and then investigate the analytic classification of the reduced models. Those reduced pairs of regular foliations are well understood. The case of a regular and a singular foliation is dealt with Mattei-Moussu's Theorem for which we provide a new proof, avoiding Gronwall's inequality. We end-up announcing results recently obtained by the first author in the case of a pair of reduced foliations sharing the same separatrices.

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Adjaratou Arame Diaw, Frank Loray. 2020-08-03. Pairs of foliations and Mattei-Moussu's theorem. https://arxiv.org/abs/2008.00719

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