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Let $g$ be a simple classical Lie superalgebra. In this talk we will
construct subalgebras with detect the relative cohomology of $g$ with
respect to $g_0$ through the use of invariant theory. This will allow us
to define rank varieties and develop a theory of support varieties for
modules over the Lie superalgebra. Later in the talk, we will indicate how
these varieties provide a geometric interpretation of the combinatorial
description of the defect of $g$ and the atypicality of simple
$g$-supermodules due to Kac and Wakimoto.
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