Margherita Barile, Marcel Morales

On unions of scrolls along linear spaces

Rend. Semin. Mat. Univ. Padova 111 (2004), 161-178.

This paper is a follow-up to a previous article of ours. There we gave an  explicit constructive characterization of all equidimensional ideals of  minimal degree defining varieties other than quadric hypersurfaces and cones  over the Veronese surface in P^5. This is the third class of minimal  varieties occurring in the classification resulting from the contributions of  various authors: it consists of unions of scrolls embedded in linear  subspaces - we will call this a  scroller - and was discovered by Xambo'. He proved that, in the equidimensional case,  these varieties have mimimal  degree under the additional assumption that they be connected in codimension  1. In Section 2 we modify the argumentation  used in our previous paper in  order to show that this  property can be removed from the hypotheses, since it is fulfilled by all equidimensional scrollers of minimal degree. In  Section 3 we give a constructive method for all defining ideals of  scrollers.