On the envelope of a vector field

Tom 94 / 2011

Bernard Malgrange Banach Center Publications 94 (2011), 239-246 MSC: Primary 37C10; Secondary 34Lxx. DOI: 10.4064/bc94-0-17

Streszczenie

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.

Autorzy

  • Bernard MalgrangeUFR de Mathématiques, UMR 5582
    Institut Fourier, Université Grenoble 1 - CNRS
    38402 Saint-Martin d'Hères Cedex, France
    e-mail

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