  We show that compactness of the $\overline{\partial}$-Neumann operator is
independent of the metric, and we give a new proof of this independence for
subellipticity. We define an abstract obstruction to compactness, namely the
common zero set of all the compactness multipliers, and we identify this subset
of the boundary for convex domains in $\mathbb{C}^{n}$ and for complete Hartogs
domains in $\mathbb{C}^{2}$.
