A singular Darboux type theorem and non-integrable projective distributions of degree one

Abstract

We prove a singular Darboux type theorem for homogeneous polynomial closed $2$-forms of degree one on ${\mathbb{C}}^n$. As application, we classify non-integrable codimension one distributions, of degree one, and arbitrary classes on projective spaces.

To Omegar Calvo-Andrade on the occasion of his 60th birthday; Major changes following suggestions of the referee