On the realization of orbit closures as support varieties

Let G be a reductive algebraic group over an algebraically closed field k   of characteristic p>0p>0 with g=Lie(G)g=Lie(G). In this paper the authors investigate the following problem. Given a nilpotent orbit OO in the restricted nullcone N1(g)N1(g), construct a finite-dimensional (tilting) G-module such that the support variety of M  , Vg(M)Vg(M), is the closure of OO.