Holomorphic Koszul-Brylinski Homology

Abstract

In this note, we study the Koszul-Brylinski homology of holomorphic Poisson manifolds. We show that it is isomorphic to the cohomology of a certain smooth complex Lie algebroid with values in the Evens-Lu-Weinstein duality module. As a consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinski homology is nondegenerate. Finally we compute the Koszul-Brylinski homology for Poisson structures on $\CP^1\times\CP^1$.

14 pages

References in corpus (5)

• Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids
• Duality and equivalence of module categories in noncommutative geometry I
• Poisson (co)homology and isolated singularities
• Poisson Cohomology of Del Pezzo surfaces
• The Van den Bergh duality and the modular symmetry of a Poisson variety

Cited by in corpus (4)

• Poisson Cohomology of Del Pezzo surfaces
• Poisson structures on almost complex Lie algebroids
• Geometry of Maurer-Cartan Elements on Complex Manifolds
• Formality of the Dolbeault complex and deformations of holomorphic Poisson manifolds