On the envelope of a vector field
Volume 94 / 2011
Banach Center Publications 94 (2011), 239-246
MSC: Primary 37C10; Secondary 34Lxx.
DOI: 10.4064/bc94-0-17
Abstract
Given a vector field $X$ on an algebraic variety $V$ over $\mathbb{C}$, 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 $t=\text{constant}$). I show that either they are equal, or the second has codimension one in the first.
