  In this paper the authors introduce an analog of the nilpotent cone,
${\mathcal N}$, for a classical Lie superalgebra, ${\mathfrak g}$, that
generalizes the definition for the nilpotent cone for semisimple Lie algebras.
For a classical simple Lie superalgebra, ${\mathfrak g}={\mathfrak
g}_{\bar{0}}\oplus {\mathfrak g}_{\bar{1}}$ with $\text{Lie
}G_{\bar{0}}={\mathfrak g}_{\bar{0}}$, it is shown that there are finitely many
$G_{\bar{0}}$-orbits on ${\mathcal N}$. Later the authors prove that the
Duflo-Serganova commuting variety, ${\mathcal X}$, is contained in ${\mathcal
N}$ for any classical simple Lie superalgebra. Consequently, our finiteness
result generalizes and extends the work of Duflo-Serganova on the commuting
variety. Further applications are given at the end of the paper.

Representation Theory;Group Theory