Intrinsic Stratifications of Analytic Varieties

TL;DR

This paper introduces a coordinate-free method to construct a stratification of an analytic variety using a Lie algebra of germs of vector fields, proving it forms a Nagano foliation.

Contribution

It establishes that the Nagano foliation of an analytic variety is a stratification, utilizing the Oka-Cartan-Serre theory without coordinate dependence.

Findings

Nagano foliation forms a stratification of the variety

Construction relies on Lie algebra of germs of vector fields

Uses Oka-Cartan-Serre theory for proof

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.