  We advocate that a generalized Kronheimer construction of the K\"ahler
quotient crepant resolution $\mathcal{M}_\zeta \longrightarrow
\mathbb{C}^3/\Gamma$ of an orbifold singularity where $\Gamma\subset
\mathrm{SU(3)}$ is a finite subgroup naturally defines the field content and
interaction structure of a superconformal Chern-Simons Gauge Theory. This is
supposedly the dual of an M2-brane solution of $D=11$ supergravity with
$\mathbb{C}\times\mathcal{M}_\zeta$ as transverse space. We illustrate and
discuss many aspects of this of constructions emphasizing that the equation
$\pmb{p}\wedge\pmb{p}=0$ which provides the K\"ahler analogue of the
holomorphic sector in the hyperK\"ahler moment map equations canonically
defines the structure of a universal superpotential in the CS theory. The
kernel of the above equation can be described as the orbit with respect to a
quiver Lie group $\mathcal{G}_\Gamma$ of a locus $L_\Gamma \subset
\mathrm{Hom}_\Gamma(\mathcal{Q}\otimes R,R)$ that has also a universal
definition. We discuss the relation between the coset manifold
$\mathcal{G}_\Gamma/\mathcal{F}_\Gamma$, the gauge group $\mathcal{F}_\Gamma$
being the maximal compact subgroup of the quiver group, the moment map
equations and the first Chern classes of the tautological vector bundles that
are in a one-to-one correspondence with the nontrivial irreps of $\Gamma$.
These first Chern classes provide a basis for the cohomology group
$H^2(\mathcal{M}_\zeta)$. We discuss the relation with conjugacy classes of
$\Gamma$ and provide the explicit construction of several examples emphasizing
the role of a generalized McKay correspondence. The case of the ALE manifold
resolution of $\mathbb{C}^2/\Gamma$ singularities is utilized as a comparison
term and new formulae related with the complex presentation of Gibbons-Hawking
metrics are exhibited.
