Families and unfoldings of singular holomorphic Lie Algebroids

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