Local monomialization of a system of first integrals of Darboux type (Q1989533)

Summary: 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.