English

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 m(p)+nsm(p)+n-s 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

R2 v1 2026-06-21T13:35:07.402Z