Varieties of complexes and foliations

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 \(\mathcal F(r, d)\).