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A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2006Embargo end date: 01 Jan 2005Publisher:Cambridge University Press (CUP)Journal:Glasgow Mathematical Journal, volume 48, pages 459-462 (issn: 0017-0895, eissn: 1469-509X,

Authors: Bernt Tore Jensen; William Crawley-Boevey;

doi: 10.1017/s0017089506003259 , 10.48550/arxiv.math/0505149

arXiv: http://arxiv.org/abs/math/0505149

A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES

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Abstract

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.

4 pages, various improvements

Related Organizations

University of Leeds
United Kingdom
Université de Sherbrooke
Canada

Keywords

Mathematics - Algebraic Geometry, FOS: Mathematics, Algebraic Geometry (math.AG)

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