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A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES

Published online by Cambridge University Press:  06 December 2006

WILLIAM CRAWLEY-BOEVEY  and
BERNT TORE JENSEN
WILLIAM CRAWLEY-BOEVEY
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS29JT, United Kingdom
BERNT TORE JENSEN
Affiliation:
Département de mathématiques, Faculté des Sciences, Université de Sherbrooke, 2500 boul. de l'Université, Sherbrooke (Quebec) J1K 2R1, Canada e-mail: Bernt.Tore.Jensen@USherbrooke.ca
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Abstract

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It is easy to imagine that a subvariety of a vector bundle, whose intersection with every fibre is a vector subspace of constant dimension, must necessarily be a sub-bundle. We give two examples to show that this is not true, and several situations in which the implication does hold. For example it is true if the base is normal and the field has characteristic zero. A convenient test is whether or not the intersections with the fibres are reduced as schemes.

Keywords

14F05
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 48 , Issue 3 , September 2006 , pp. 459 - 462
Copyright
2006 Glasgow Mathematical Journal Trust