Deformations of Complex 3-Dimensional Associative Algebras

Alice Fialowski,Michael Pen

Abstract

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.