Holomorphic Koszul-Brylinski homology via Dolbeault cohomology
Abstract
We use the Dolbeault cohomology to investigate the Koszul-Brylinski homology on holomorphic Poisson manifolds. We obtain the Leray-Hirsch theorem for Hochschild homology and the Mayer-Vietoris sequence, K\"unneth theorem for holomorphic Koszul-Brylinski homology. In particular, we show some relations of holomorphic Koszul-Brylinski homologies around a blow-up transformation for the general case (not necessarily compact) by our previous works on the Dolbeault cohomology.
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