  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.
