TY - JOUR
T1 - Integration of holomorphic Lie algebroids
AU - Laurent-Gengoux, Camille
AU - Stiénon, Mathieu
AU - Xu, Ping
N1 - Funding Information:
Mathieu Stiénon’s research was supported by the European Union through the FP6 Marie Curie R.T.N. ENIGMA (Contract number MRTN-CT-2004-5652). Ping Xu’s research was partially supported by NSF grants DMS-0306665 and DMS-0605725 & NSA grant H98230-06-1-0047.
PY - 2009/9
Y1 - 2009/9
N2 - 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.
AB - 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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U2 - 10.1007/s00208-009-0388-7
DO - 10.1007/s00208-009-0388-7
M3 - Article
AN - SCOPUS:70350135955
SN - 0025-5831
VL - 345
SP - 895
EP - 923
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -