Geodesic
Families of distributions and Pfaff systems under duality
Journal of Singularities, Tome 11 (2015), pp. 164-189

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A singular distribution on a non-singular variety X can be defined either by a subsheaf D of the tangent sheaf, or by the zeros of a subsheaf of 1-forms, that is, a Pfaff system. Although both definitions are equivalent under mild conditions on D, they give rise, in general, to non-equivalent notions of flat families of distributions. In this work we investigate conditions under which both notions of flat families are equivalent. In the last sections we focus on the case where the distribution is integrable, and we use our results to generalize a theorem of Cukierman and Pereira. 
@article{10_5427_jsing_2015_11g,
     author = {Federico Quallbrunn},
     title = {Families of distributions and {Pfaff} systems under duality},
     journal = {Journal of Singularities},
     pages = {164--189},
     publisher = {mathdoc},
     volume = {11},
     year = {2015},
     doi = {10.5427/jsing.2015.11g},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2015.11g/}
}
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Federico Quallbrunn. Families of distributions and Pfaff systems under duality. Journal of Singularities, Tome 11 (2015), pp. 164-189. doi: 10.5427/jsing.2015.11g

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