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.
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