A note on sub-bundles of vector bundles
代数几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0505149,
title = {A note on sub-bundles of vector bundles},
author = {William Crawley-Boevey and Bernt Tore Jensen},
journal= {arXiv preprint arXiv:math/0505149},
year = {2007}
}
备注
4 pages, various improvements