  In this paper the authors introduce a class of parabolic subalgebras for
classical simple Lie superalgebras associated to the detecting subalgebras
introduced by Boe, Kujawa and Nakano. These parabolic subalgebras are shown to
have good cohomological properties governed by the Bott-Borel-Weil theorem
involving the zero component of the Lie superalgebra in conjunction with the
odd roots. These results are later used to verify an open conjecture given by
Boe, Kujawa and Nakano pertaining to the equality of various support varieties.
