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.