Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

Details Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

2007-07-28

arxiv.org/abs/0707.4253v4

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn088, 46 pages

Mathematics

Differential Geometry

29 pages, v2: paper split into two, part 1 of 2, v3: two references added, v4: final version to appear in International Mathem

Scientific paper

10.1093/imrn/rnn088

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and describe a double complex which computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle $A\to X$ is shown to be equivalent to a matched pair of complex Lie algebroids $(T^{0,1}X,A^{1,0})$, in the sense of Lu. The holomorphic Lie algebroid cohomology of $A$ is isomorphic to the cohomology of the elliptic Lie algebroid $T^{0,1}X\bowtie A^{1,0}$. In the case when $(X,\pi)$ is a holomorphic Poisson manifold and $A=(T^*X)_\pi$, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold.

Affiliated with

Also associated with

No associations

Rating

Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-396177