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 $\mathcal F(r, d)$.

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