Holomorphic Poisson Manifolds and Holomorphic Lie Algebroids

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dc.creatorLaurent-Gengoux, Camille
dc.creatorStienon, Mathieu
dc.creatorXu, Ping
dc.date2007-07-28
dc.date2008-07-14
dc.date.accessioned2026-07-07T10:06:56Z
dc.date.available2026-07-07T10:06:56Z
dc.descriptionWe 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 $(X,π)$ is a holomorphic Poisson manifold and $A=(T^*X)_π$, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold.
dc.description29 pages, v2: paper split into two, part 1 of 2, v3: two references added, v4: final version to appear in International Mathematics Research Notices
dc.identifierhttps://arxiv.org/abs/0707.4253
dc.identifierhttp://arxiv.org/abs/0707.4253
dc.identifierInternational Mathematics Research Notices (2008) Vol. 2008 : article ID rnn088, 46 pages
dc.identifierdoi:10.1093/imrn/rnn088
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170461
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.titleHolomorphic Poisson Manifolds and Holomorphic Lie Algebroids
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