Integration of holomorphic Lie algebroids |
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| Authors: | Camille Laurent-Gengoux Mathieu Stiénon Ping Xu |
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| Institution: | 1.Département de mathématiques,Université de Poitiers,Futuroscope-Chasseneuil,France;2.Departement Mathematik,E.T.H. Zürich,Zurich,Switzerland;3.Department of Mathematics,Penn State University,University Park,USA |
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| Abstract: | 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 (Theorem 4.1 in Crainic, Fernandes in Ann Math 2:157, 2003) do also apply
in the holomorphic context without any modification. As a consequence we prove that a holomorphic Poisson manifold is integrable
if and only if its real part or imaginary part is integrable as a real Poisson manifold. |
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