Projective bundle
In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. Every vector bundle over a variety X gives a projective bundle by taking the projective spaces of the fibers, but not all projective bundles arise in this way: there is an obstruction in the cohomology group H2(X,O*).
The projective bundle of a vector bundle E is the same thing as the Grassmannian bundle 
of 1-planes in E.
See also
References
- Elencwajg, G.; Narasimhan, M. S. (1983), "Projective bundles on a complex torus", Journal für die reine und angewandte Mathematik 340: 1–5, doi:10.1515/crll.1983.340.1, ISSN 0075-4102, MR 691957
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