Candidates for anti-de Sitter Horizons

We find, from the toric description of the moduli space of D3-branes on non-compact six-dimensional singularities ${\text{C}}^3\mathrm{/}{\mathbb{Z}}_3$ and ${\text{C}}^3\mathrm{/}{\mathbb{Z}}_5$ in the blown-down limit, the four-dimensional bases on which these singular spaces are complex cones, and prove the existence of K"ahler-Einstein metrics on these four-dimensional bases. This shows, in particular, that one can use the horizons obtained from these base spaces by a U(1)-foliation as compact parts of the target space for Type-IIB string theory with $\text{ads}5$ in the context of the AdS-CFT correspondence.