Local Resolution of Ideals Subordinated to a Foliation

Abstract

Let $M$ be a complex- or real-analytic manifold, $\theta$ be a singular distribution and $\mathcal{I}$ a coherent ideal sheaf defined on $M$. We prove the existence of a local resolution of singularities of $\mathcal{I}$ that preserves the class of singularities of $\theta$, under the hypothesis that the considered class of singularities is invariant by $\theta$-admissible blowings-up. In particular, if $\theta$ is monomial, we prove the existence of a local resolution of singularities of $\mathcal{I}$ that preserves the monomiality of the singular distribution $\theta$.

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References in corpus (1)

• Local monomialization of a system of first integrals of Darboux type

Cited by in corpus (2)

• Local monomialization of a system of first integrals of Darboux type
• Monomialization of a quasianalytic morphism