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

TL;DR

This paper classifies codimension one degree 3 distributions on projective three-space, detailing their Chern classes, singular schemes, and moduli spaces through stability analysis.

Contribution

It provides a comprehensive classification and existence results for such distributions, including descriptions of their moduli spaces and stability conditions.

Findings

Classification of possible Chern classes

Descriptions of singular schemes components

Existence and moduli space structures

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.