The moduli space of $2\mathrm{\mid }1$-dimensional complex associative algebras

In this paper, we study the moduli space of $2\mathrm{\mid }1$-dimensional complex associative algebras, which is also the moduli space of codifferentials on the tensor coalgebra of a $1\mathrm{\mid }2$-dimensional complex space. We construct the moduli space by considering extensions of lower dimensional algebras. We also construct miniversal deformations of these algebras. This gives a complete description of how the moduli space is glued together via jump deformations.