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arXiv · 2204.02600

Holomorphic Koszul-Brylinski homology via Dolbeault cohomology

Lingxu Meng
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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\"{u}nneth 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.

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Lingxu Meng. 2022-04-06. Holomorphic Koszul-Brylinski homology via Dolbeault cohomology. https://doi.org/10.1007/s10711-022-00752-0

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