Revista Matemática Iberoamericana


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Volume 34, Issue 3, 2018, pp. 967–1000
DOI: 10.4171/RMI/1012

Published online: 2018-08-27

Local monomialization of a system of first integrals of Darboux type

André Belotto da Silva[1]

(1) Université de Toulouse III Paul Sabatier, Toulouse, France

Given a real- or complex-analytic singular foliation $\theta$ with $n$ first integrals of meromorphic or Darboux type $(f_1,\dots,f_n)$, we prove that there exists a local monomialization of the first integrals. In particular, if $\theta$ is generated by the $n$ first integrals, we prove the existence of a local reduction of singularities of $\theta$ to monomial singularities.

Keywords: First integrals, monomialization, reduction of singularities, singular foliations

Belotto da Silva André: Local monomialization of a system of first integrals of Darboux type. Rev. Mat. Iberoamericana 34 (2018), 967-1000. doi: 10.4171/RMI/1012