Degenerations of 3-dimensional nilpotent associative algebras over an algebraically closed field

Abstract

We determine the complete degeneration picture inside the variety of nilpotent associative algebras of dimension 3 over an algebraically closed field of characteristic not equal to 2. Comparing with the discussion in [Ivanova N.M. and Pallikaros C.A., Degenerations of complex associative algebras of dimension three via Lie and Jordan algebras, {\it Advances in Group Theory and Applications}, 18 (2024), 41-79], for some of the arguments in the present article we needed to develop alternative techniques which are now valid over an arbitrary algebraically closed field. There is a dichotomy of cases concerning the results obtained, corresponding to whether the characteristic of the field is 2 or not.