| Let F=F(r, d) denote the algebraic variety parametrizing integrable differential 1-forms of degree d in the complex projective space of dimension r. We study the geometry of this variety, in particular the problem of determining its irreducible components. Let C denote the variety parametrizing differential complexes on vector spaces of given dimensions. We shall review the definition and basic properties of C, including the description of its irreducible components. Then we shall represent F as a certain linear section of C. Finally, we discuss the relation with the irreducible components of F. |