  We define the associated variety $ X_{M} $ of a module $ M $ over a
finite-dimensional superalgebra $ {\mathfrak g} $, and show how to extract
information about $ M $ from these geometric data. $ X_{M} $ is a subvariety of
the cone $ X $ of self-commuting odd elements.
  For finite-dimensional $ M $, $ X_{M} $ is invariant under the action of the
underlying Lie group $ G_{0} $. For simple superalgebra with invariant
symmetric form, $ X $ has finitely many $ G_{0} $-orbits; we associate a number
(rank) to each such orbit. One can also associate a number (degree of
atypicality) to an irreducible finite-dimensional representation.
  We prove that if $ M $ is an irreducible $ {\mathfrak g} $-module of degree
of atypicality $ k $, then $ X_{M} $ lies in the closure of all orbits on $ X $
of rank $ k $. If $ {\mathfrak g}={\mathfrak g}{\mathfrak l}(m|n) $ we prove
that $ X_{M} $ coincides with this closure.
