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Gradient-like vector fields on a complex analytic variety

Cheol-Hyun Cho Giovanni Marelli

Geometric Analysis and Geometric Topology mathscidoc:1912.43243

arXiv preprint arXiv:0908.1862, 2009.8
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)+ ns as was conjectured by Goresky and MacPherson.
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@inproceedings{cheol-hyun2009gradient-like,
  title={Gradient-like vector fields on a complex analytic variety},
  author={Cheol-Hyun Cho, and Giovanni Marelli},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113144797760803},
  booktitle={arXiv preprint arXiv:0908.1862},
  year={2009},
}
Cheol-Hyun Cho, and Giovanni Marelli. Gradient-like vector fields on a complex analytic variety. 2009. In arXiv preprint arXiv:0908.1862. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113144797760803.
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