The moduli space of 4-dimensional nilpotent complex associative algebras

In this paper, we study 4-dimensional nilpotent complex associative algebras. This is a continuation of the study of the moduli space of 4-dimensional algebras. The nonnilpotent algebras were analyzed in an earlier paper. Even though there are only 15 families of nilpotent 4-dimensional algebras, the complexity of their behavior warranted a separate study, which we give here.