A bstract We construct and study the supersymmetry properties of the weighted projective spaces 𝕎ℂℙ 2 and 𝕎ℂℙ 3 . These are topologically ℂℙ n with n + 1 orbifold singularities and as such are higher dimensional analogues of the “spindle” or 𝕎ℂℙ 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, 𝕎ℂℙ 2 and 𝕎ℂℙ 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 × 𝕎ℂℙ 2 × S 1 and AdS 4 × 𝕎ℂℙ 3 via duality, in which 𝕎ℂℙ n appears without a connection fibred over it. We also leverage our results to construct a supersymmetric AdS 3 solution containing a topological 𝕋 (1,1) space with 4 orbifold singularities.
Conti et al. (Tue,) studied this question.
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