Gradient-like vector fields on a complex analytic variety

Cheol-Hyun Cho; Giovanni Marelli

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arXiv · 0908.1862

Gradient-like vector fields on a complex analytic variety

Cheol-Hyun Cho·Giovanni Marelli

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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 $m(p)+n-s$ as was conjectured by Goresky and MacPherson.

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Cheol-Hyun Cho, Giovanni Marelli. 2009-08-13. Gradient-like vector fields on a complex analytic variety. https://arxiv.org/abs/0908.1862

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