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

TL;DR

This paper proves a singular Darboux type theorem for certain polynomial 2-forms and classifies non-integrable degree-one distributions on projective spaces, advancing understanding of complex geometric structures.

Contribution

It introduces a singular Darboux theorem for degree-one polynomial 2-forms and classifies non-integrable codimension one distributions of degree one on projective spaces.

Findings

Established a singular Darboux theorem for polynomial 2-forms

Classified non-integrable degree-one distributions on projective spaces

Provided new insights into complex geometric structures

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.