Holomorphic Koszul-Brylinski homology via Dolbeault cohomology
arXiv:2204.02600 · doi:10.1007/s10711-022-00752-0
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, Künneth 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 (\emph{not necessarily compact}) by our previous works on the Dolbeault cohomology.
15 pages