A note on sub-bundles of vector bundles

Research paper by William Crawley-Boevey, Bernt Tore Jensen

Indexed on: 02 May '06Published on: 02 May '06Published in: Mathematics - Algebraic Geometry


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.