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.
On the ampleness of the normal bundle of line congruences / E. Arrondo, M. Bertolini, C. Turrini. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 23:2(2011), pp. 223-244.
On the ampleness of the normal bundle of line congruences
M. BertoliniSecondo
;C. TurriniUltimo
2011
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.
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