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 unfoldings of Lie algebroids, which generalizes the theory of singular holomorphic foliations developed by T. Suwa. We show that a one-to-one correspondence between transversal unfoldings and holomorphic flat connections on a natural Lie algebroid on the bases exists.