Integration of holomorphic Lie algebroids

Camille Laurent-Gengoux, Mathieu Stiénon, Ping Xu

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16 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)895-923
Number of pages29
JournalMathematische Annalen
Volume345
Issue number4
DOIs
StatePublished - Sep 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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