On unions of scrolls along linear spaces (Q2504923)

Summary: According to the classification resulting from the successive contributions by Bertini, Del Pezzo and \textit{S. Xambó} [Collect. Math. 32, 149--163 (1981; Zbl 0501.14020)], the equidimensional varieties of minimal degree which are connected in codimension one are of three types: quadric hypersurfaces, cones over the Veronese surface in \(\mathbb{P}^5\) and unions of scrolls embedded in linear subspaces. In this paper we give a complete constructive characterization of the ideals defining varieties of the latter type, which were presented in [loc. cit]. We also show that for these varieties, equidimensionality and minimal degree imply connectivity in codimension one, which provides a better understanding of the results in [loc. cit.]. Finally we give a complete description of all rulings of a scroll. Throughout the paper we deal with projective varieties not contained in any hyperplane.