Varieties of complexes and foliations

TL;DR

This paper studies the moduli space of algebraic foliations, showing it can be represented as a linear section of a variety of complexes, which helps understand its irreducible components.

Contribution

It introduces a new representation of the moduli space of foliations as a linear section of a variety of complexes, providing insights into its structure.

Findings

Representation of $\

Information on irreducible components of $\

Connection between foliations and varieties of complexes.

Abstract

Let $\mathcal F(r, d)$ denote the moduli space of algebraic foliations of codimension one and degree $d$ in complex proyective space of dimension $r$. We show that $\mathcal F(r, d)$ may be represented as a certain linear section of a variety of complexes. From this fact we obtain information on the irreducible components of $\mathcal F(r, d)$.