Enrique Arrondo Esteban

Congruences of small degree in G(1,4)

We give the list of all possible congruences in G(1,4) of degree d less than or equal to 10 and we explicitely construct most of them.

On the ampleness ofthe 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 . Making use of some results on the geometry of the focal loci of congruences ([Arrondo, Bertolini and Turrini, Asian J. of Math. 5: 535–560, 2001] and [Arrondo, Bertolini and Turrini, Asian J. of Math. 9: 449–472, 2005]), 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 .