Holomorphic Koszul-Brylinski Homology

Details Holomorphic Koszul-Brylinski Homology Holomorphic Koszul-Brylinski Homology

2009-03-29

arxiv.org/abs/0903.5065v1

Int. Math. Res. Not. IMRN 2011, no. 3, 553-571

Mathematics

Differential Geometry

14 pages

Scientific paper

10.1093/imrn/rnq084

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 $\CP^1\times\CP^1$.

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