Holomorphic Koszul-Brylinski homologies of Poisson blow-ups

Xiaojun Chen; Youming Chen; Song Yang; Xiangdong Yang

Holomorphic Koszul-Brylinski homologies of Poisson blow-ups

Differential Geometry 2025-07-21 v3

Authors: Xiaojun Chen , Youming Chen , Song Yang , Xiangdong Yang

Abstract

We derive a blow-up formula for holomorphic Koszul-Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the $E_{1}$ -degeneracy of the Dolbeault-Koszul-Brylinski spectral sequence under Poisson blow-ups, and compute the holomorphic Koszul-Brylinski homology for del Pezzo surfaces and two complex nilmanifolds with holomorphic Poisson structures.

Keywords

holomorphic koszul-brylinski homology poisson blow-up compact holomorphic poisson manifold dolbeault-koszul-brylinski spectral sequence del pezzo surface complex nilmanifold

Cite

@article{arxiv.2202.09764,
  title  = {Holomorphic Koszul-Brylinski homologies of Poisson blow-ups},
  author = {Xiaojun Chen and Youming Chen and Song Yang and Xiangdong Yang},
  journal= {arXiv preprint arXiv:2202.09764},
  year   = {2025}
}

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29 pages.Comments are welcome!

Holomorphic Koszul-Brylinski homologies of Poisson blow-ups

Abstract

Keywords

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