Abstract
We prove that the Hilbert scheme of points on a normal quasi-projective surface with at worst Kleinian singularities is irreducible.
Acknowledgments
Xudong Zheng thanks Professor Lawrence Ein for the many valuable suggestions on this work. He thanks Professor Frank-Olaf Schreyer for pointing out the approach to understand deformations of reflexive modules. He is also grateful to Professors Izzet Coskun, Kevin Tucker, and the anonymous referee for wonderful suggestions and comments.