Deformation of 2-step Nilmanifolds with Abelian Complex Structures
  We develop deformation theory for abelian invariant complex structures on a nilmanifold, and prove that in this case the invariance property is preserved by the Kuranishi process. A purely algebraic condition characterizes the deformations leading again to abelian structures, and we prove that such deformations are unobstructed. Various examples illustrate the resulting theory, and the behavior possible in 3 complex dimensions. 
C. McLaughlin, H. Pedersen, Y. S. Poon, S. Salamon