2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70067We 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.Differential GeometryAlgebraic Geometry32G05; 53C15, 53C56, 57S25, 17B30text