  We give algebraic and geometric classifications of $6$-dimensional complex
nilpotent anticommutative algebras. Specifically, we find that, up to
isomorphism, there are $14$ one-parameter families of $6$-dimensional nilpotent
anticommutative algebras, complemented by $130$ additional isomorphism classes.
The corresponding geometric variety is irreducible and determined by the
Zariski closure of a one-parameter family of algebras. In particular, there are
no rigid $6$-dimensional complex nilpotent anticommutative algebras.
