Families of Distributions and Pfaff systems under duality

FEDERICO QUALLBRUNN

New York

Congreso; Foliation Theory in Algebraic Geometry; 2013

Simons Foundation

A singular distribution on a non-singular variety X can be defined either by a subsheaf D ⊆ T X of the tangent sheaf, or by the zeros of a subsheaf D0 ⊆ Ω1 X of 1-forms. 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 notionsof flat families are equivalent