Local resolution of ideals subordinated to a foliation

Original Paper
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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 \(\theta \).

Keywords

Foliation Resolution of singularities Monomial 

Mathematics Subject Classification

32S45 14E15 
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Notes

Acknowledgments

I would like to thank Edward Bierstone for the useful suggestions and for reviewing the manuscript. The structure of this manuscript is strongly influenced by him. I would also like to express my gratitude to Daniel Panazzolo for the useful discussions concerning the problem and its applications. Finally, I would like to thank the anonymous reviewer for several very useful comments and, in particular, for suggesting a different title for the manuscript.

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Copyright information

© Springer-Verlag Italia 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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