Given a compact affine nonsingular real algebraic variety X and a nonsingular subvariety Z C X belonging to a large class of subvarieties, we show how to embed X in a suitable Grassmannian so that Z becomes the transverse intersection of the zeros of a section of the tautological bundle on the Grassmannian.
@article{urn:eudml:doc:44200,
title = {Embedding of real varieties and their subvarieties into Grassmannians.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {8},
year = {1995},
pages = {265-268},
zbl = {0868.14030},
mrnumber = {MR1367930},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44200}
}
Buchner, M. A. Embedding of real varieties and their subvarieties into Grassmannians.. Revista Matemática de la Universidad Complutense de Madrid, Tome 8 (1995) pp. 265-268. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44200/