Gradient-like vector fields on a complex analytic variety
Geometric Topology
2010-08-02 v3 Algebraic Geometry
Abstract
Given a complex analytic function f on a Whitney stratified complex analytic variety of complex dimension n, whose real part Re(f) is Morse, we prove the existence of a stratified gradient-like vector field for Re(f) such that the unstable set of a critical point p on a stratum S of complex dimension s has real dimension as was conjectured by Goresky and MacPherson.
Keywords
Cite
@article{arxiv.0908.1862,
title = {Gradient-like vector fields on a complex analytic variety},
author = {Cheol-Hyun Cho and Giovanni Marelli},
journal= {arXiv preprint arXiv:0908.1862},
year = {2010}
}
Comments
23 pages, 4 figure, v2:major revision, v3:added restriction on Morse function and removed fast condition