Support varieties of baby Verma modules

Let G be a connected reductive algebraic group over an algebraically closed field k of prime characteristic p and g = Lie(G). For a given nilpotent p-character χ ∈ g, let Zχ(λ) be a baby Verma module associated with a restricted weight ?. A conjecture describing the support variety of Zχ(λ) via that of its restricted counterpart is given: Vg(Zχ(λ)) = Vg(Z0(λ)) n zg(λ). Under the assumption of p = h(the Coxeter number) and χ p-regular, this conjecture is proved when χ falls in the regular nilpotent orbit for any g and the subregular nilpotent orbit for g being of type An. We also verify this conjecture whenever g is of type An and χ falls in the minimal nilpotent orbit.