Families and unfoldings of singular holomorphic Lie Algebroids

TL;DR

This paper explores the structure and deformations of singular holomorphic Lie algebroids on complex spaces, establishing a correspondence between unfoldings and flat connections, thus advancing the understanding of their geometric properties.

Contribution

It introduces the concept of unfoldings for singular holomorphic Lie algebroids and establishes a correspondence with holomorphic flat connections, generalizing foliation theory.

Findings

Establishes a one-to-one correspondence between transversal unfoldings and flat connections.

Generalizes the theory of singular holomorphic foliations.

Provides new insights into the deformation theory of Lie algebroids.

Abstract

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.