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On the ampleness of the normal bundle of line congruences
-
Enrique Arrondo
,
Marina Bertolini
Published/Copyright:
April 2, 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 
. 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
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Articles in the same Issue
- On the ampleness of the normal bundle of line congruences
- Topological types of 3-dimensional small covers
- Null controllability with constraints on the state for nonlinear heat equations
- Exponential closing property and approximation of Lyapunov exponents of linear cocycles
- Reflection systems and partial root systems
- Todd's maximum-volume ellipsoid problem on symmetric cones
- Refinement of the spectral asymptotics of generalized Krein Feller operators
