Holomorphic Koszul-Brylinski homologies of Poisson blow-ups
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 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.
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