Intrinsic Stratifications of Analytic Varieties
Differential Geometry
2014-02-19 v3 Analysis of PDEs
Complex Variables
Abstract
By attaching a Lie algebra of germs of analytic vector fields to every point of a (real or complex) analytic variety V we construct the Nagano foliation of the variety. We prove that the Nagano foliation of V is a stratification. The treatment of the subject is totally coordinate free but relies on the Oka-Cartan-Serre theory of coherent analytic sheaves.
Cite
@article{arxiv.1402.0179,
title = {Intrinsic Stratifications of Analytic Varieties},
author = {François Treves},
journal= {arXiv preprint arXiv:1402.0179},
year = {2014}
}
Comments
The Nagano foliation as defined in the paper Intrinsic Stratifications of Analytic Varieties is not locally finite. I am indebted to Prof. Terence The Nagano foliation as I have defined it is not always locally finite. I am indebted to Prof. Gaffney for pointing out to me the counter-example of the 4 moving lines in C^3