A bstract We construct and study the supersymmetry properties of the weighted projective spaces πββ 2 and πββ 3 . These are topologically ββ n with n + 1 orbifold singularities and as such are higher dimensional analogues of the βspindleβ or πββ 1 . We use these to construct interesting supersymmetric orbifolds of canonical near horizon geometries of relevance to the AdS/CFT correspondence. Interestingly, for certain tunings of their integer weights, and unlike the spindle, πββ 2 and πββ 3 are compatible with supersymmetry beyond the realm of gauged supergravity. This allows one to construct interesting supersymmetric solutions in type II supergravity such as AdS 5 Γ πββ 2 Γ S 1 and AdS 4 Γ πββ 3 via duality, in which πββ n appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS 3 solution containing a topological π (1,1) space with 4 orbifold singularities.
Conti et al. (Tue,) studied this question.