Resumen de Local monomialization of a system of first integrals of Darboux type

André Belotto da Silva

• Given a real- or complex-analytic singular foliation θ with n first integrals of meromorphic or Darboux type (f1,…,fn), we prove that there exists a local monomialization of the first integrals. In particular, if θ is generated by the n first integrals, we prove the existence of a local reduction of singularities of θ to monomial singularities.