Codimension one distributions of degree 3 on the three-dimensional projective space

Abstract

We make a classification of codimension one degree 3 distributions on the projective three space, giving possible Chern classes of the tangent sheaf and describing de zero and one dimensional components of the singular scheme of the distribution. Also, we show the existence and describe some moduli spaces of such distributions, using the concept of stability of the tangent sheaf.