On the ampleness of the normal bundle of line congruences

Abstract

In this paper we study the normal bundle of the embedding of subvarieties of dimension n - 1 in the Grassmann variety of lines in P(n). Making use of some results on the geometry of the focal loci of congruences ([4] and [5]), we give some criteria to decide whether the normal bundle of a congruence is ample or not. Finally we apply these criteria to the line congruences of small degree in P(3).