Families of distributions and Pfaff systems under duality

Journal of Singularities
volume 11 (2015), 164-189

Received 20 June 2014. Received in revised form 10 August 2014.

DOI: 10.5427/jsing.2015.11g

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Abstract:

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.

Keywords:

Coherent Sheaves, Flat Families, Algebraic Foliations, Moduli Spaces, Kupka Singularities

Author(s) information:

Federico Quallbrunn
Departamento de Matemática, FCEyN
Universidad de Buenos Aires
Ciudad Universitaria, Pabellón 1
Buenos Aires (Argentina)
email: fquallb@dm.uba.ar