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Licensed Unlicensed Requires Authentication Published by De Gruyter April 2, 2011

On the ampleness of the normal bundle of line congruences

Enrique Arrondo, Marina Bertolini and Cristina Turrini
From the journal

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 .

Received: 2008-06-16
Revised: 2009-03-13
Published Online: 2011-04-02
Published in Print: 2011-March

© de Gruyter 2011