Given a vector field X on an algebraic variety V over ℂ, I compare the following two objects: (i) the envelope of X, the smallest algebraic pseudogroup over V whose Lie algebra contains X, and (ii) the Galois pseudogroup of the foliation defined by the vector field X + d/dt (restricted to one fibre t = constant). I show that either they are equal, or the second has codimension one in the first.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-17,
author = {Bernard Malgrange},
title = {On the envelope of a vector field},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {239-246},
zbl = {1246.37038},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-17}
}
Bernard Malgrange. On the envelope of a vector field. Banach Center Publications, Tome 95 (2011) pp. 239-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-17/