Higgs Branches of rank-0 5d theories from M-theory on (Aj, Al) and (Ak, Dn) singularities

We study the dynamics of M-theory on isolated non-toric Calabi-Yau threefold singularities type $(A_j,A_l)$ and $(A_k,D_n)$, engineering five-dimensional rank-zero SCFTs. Our approach consists in mapping these backgrounds to IIA string theory with D6 branes at angles O6$^{-}$ planes, computing open modes located brane intersections. This permits us characterize Higgs Branches theories as algebraic varieties, determine flavour gauge group inspect subtleties related T-branes. methods apply for all considered singularities: we give a closed formula Branches, tables $(A_k,D_n)$ series.