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<p>We derive a blow-up formula for holomorphic Koszul–Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the <i>E</i><sub>1</sub>-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.</p>

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Holomorphic Koszul–Brylinski Homologies of Poisson Blow-ups

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Xiaojun Chen,
  • Youming Chen,
  • Song Yang,
  • Xiangdong Yang

摘要

We derive a blow-up formula for holomorphic Koszul–Brylinski homologies of compact holomorphic Poisson manifolds. As applications, we investigate the invariance of the E1-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.