Minimal Model of a Nilmanifold and Moduli Space of Complex Structures

For an arbitrary real nilpotent Lie algebra (nilmanifold) with an integrable complex structure, we propose an algorithm for constructing a special model of this nilmanifold that includes information on the complex structure. As a main application, we obtain a classification of eight-dimensional $2$-generated nilpotent Lie algebras that admit an integrable complex structure. We also describe the moduli spaces of complex structures for each Lie algebra from the resulting classification list.