Abstract
We give a geometric classification of complex [Formula: see text]-dimensional nilpotent [Formula: see text]-algebras. The corresponding geometric variety has dimension 18 and decomposes into [Formula: see text] irreducible components determined by the Zariski closures of a two-parameter family of algebras and a four-parameter family of algebras. In particular, there are no rigid [Formula: see text]-dimensional complex nilpotent [Formula: see text]-algebras.
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