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Compactification of M-theory and of IIB string theory on threefold canonicalsingularities gives rise to superconformal field theories (SCFTs) in 5d and 4d,respectively. The resolutions and deformations of the singularities encodesalient features of the SCFTs and of their moduli spaces. In this paper, webuild on Part 0 of this series (arXiv:2007.15600) and further explore thephysics of SCFTs arising from isolated hypersurface singularities. We study indetail these canonical isolated hypersurface singularities that admit a smoothCalabi-Yau (crepant) resolution. Their 5d and 4d physics is discussed and their3d reduction and mirrors (the magnetic quivers) are determined in many cases.As an explorative tool, we provide a Mathematica code which computes keyquantities for any canonical isolated hypersurface singularity, including the5d rank, the 4d Coulomb branch spectrum and central charges, higher-formsymmetries in 4d and 5d, and crepant resolutions.

Coulomb and Higgs Branches from Canonical Singularities, Part 1: Hypersurfaces with Smooth Calabi-Yau Resolutions