On the construction of some Buchsbaum varieties and the Hilbert scheme of elliptic scrolls in P⁵

We study the degeneracy loci of general bundle morphisms from the direct sum of m copies of the structural sheaf on $P^n$ to $\Omega(2)$, also from the point of view of the classical geometrical interpretation of the sections of $\Omega(2)$ as linear line complexes. We consider in particular the case of $P^5$ with m=2, 3. For n=5 and m=3 we give an explicit description of the Hilbert scheme H of elliptic normal scrolls in $P^5$, by defining a natural rational map from the Grassmannian G(2,14) to H, which results to be dominant with general fibre of degree four.