We study deformations and the moduli space of 3-dimensional complex associative algebras. We use extensions to compute the moduli space, and then give a decomposition of this moduli space into strata consisting of complex projective orbifolds, glued together through jump deformations. The main purpose of this paper is to give a logically organized description of the moduli space, and to give an explicit description of how the moduli space is constructed by extensions.
"Deformations of Complex 3-Dimensional Associative Algebras." J. Gen. Lie Theory Appl. 5 1 - 22, 2011. https://doi.org/10.4303/jglta/G110102