Local monomialization of a system of first integrals of Darboux type

Abstract

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.

This version has been accepted in Revista Matematica Iberoamericana (in October 2016)

References in corpus (2)

• Local Resolution of Ideals Subordinated to a Foliation
• Local monomialization conjecture of a singular foliation of Darboux type

Cited by in corpus (2)

• Local Resolution of Ideals Subordinated to a Foliation
• Local monomialization conjecture of a singular foliation of Darboux type