# Holomorphic Koszul-Brylinski Homology - Mathematics > Differential Geometry

Abstract: In this note, we study the Koszul-Brylinski homology of holomorphic Poissonmanifolds. We show that it is isomorphic to the cohomology of a certain smoothcomplex Lie algebroid with values in the Evens-Lu-Weinstein duality module. Asa consequence, we prove that the Evens-Lu-Weinstein pairing on Koszul-Brylinskihomology is nondegenerate. Finally we compute the Koszul-Brylinski homology forPoisson structures on $\CP^1\times\CP^1$.

Author: Mathieu Stienon

Source: https://arxiv.org/