Varieties of complexes and foliations

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 $\mathcal{F}(r,d)$.