4d N=2 SCFT and singularity theory Part III: Rigid singularity

We classify three fold isolated quotient Gorenstein singularity $C^3\mathrm{/}G$. These singularities are rigid, i.e. there is no non-trivial deformation, and we conjecture that they define 4d $\mathcal{N}=2$ SCFTs which do not have a Coulomb branch.