Integration of Holomorphic Lie Algebroids

Details Integration of Holomorphic Lie Algebroids Integration of Holomorphic Lie Algebroids

2008-03-13

arxiv.org/abs/0803.2031v2

Math. Ann. (2009) 345:895--923

Mathematics

Differential Geometry

26 pages, second part of arXiv:0707.4253 which was split into two, v2: example 3.19 and section 3.7 added

Scientific paper

10.1007/s00208-009-0388-7

We prove that a holomorphic Lie algebroid is integrable if, and only if, its underlying real Lie algebroid is integrable. Thus the integrability criteria of Crainic-Fernandes do also apply in the holomorphic context without any modification. As a consequence we give another proof of the following theorem: a holomorphic Poisson manifold is integrable if, and only if, its real (or imaginary) part is integrable as a real Poisson manifold.

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