Families and unfoldings of singular holomorphic Lie Algebroids

Abstract

In this paper, we investigate families of singular holomorphic Liealgebroids on complex analytic spaces. We introduce and study a special typeof deformation called by unfoldings of Lie algebroids which generalizes thetheory due to Suwa for singular holomorphic foliations. We show that there isa one to one correspondence between transversal unfoldings and holomorphicflat connections on a natural Lie algebroid on the bases.