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, 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.

arXiv comment15 pages

References in corpus (8)

• Instantons, Poisson structures and generalized Kaehler geometry
• On the quantization of isomonodromic deformations on the torus
• Poisson Cohomology of Del Pezzo surfaces
• Constructions and classifications of projective Poisson varieties
• Poisson Cohomology of holomorphic toric Poisson manifolds. I
• Hypercohomologies of truncated twisted holomorphic de Rham complexes
• Leray-Hirsch theorem and blow-up formula for Dolbeault cohomology
• A Hodge-Type Decomposition of Holomorphic Poisson Cohomology on Nilmanifolds