Geodesic
A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES
Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 459-462

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DOI

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.
DOI : 10.1017/S0017089506003259
Mots-clés : 14F05 
CRAWLEY-BOEVEY, WILLIAM; JENSEN, BERNT TORE. A NOTE ON SUB-BUNDLES OF VECTOR BUNDLES. Glasgow mathematical journal, Tome 48 (2006) no. 3, pp. 459-462. doi: 10.1017/S0017089506003259
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