Fractional black $p$-branes on orbifold ${\mathbb{C}}^n\mathrm{/}{\mathbb{Z}}_n$

The recent discovery of an explicit solution of a black hole on the resolved orbifold ${\mathbb{C}}^n\mathrm{/}{\mathbb{Z}}_n$ makes it possible to investigate the existence of $p$-branes on the orbifold. In particular, it is possible with reasonable precision to verify the prediction that an M2-brane on ${\mathbb C}^4/{\mathbb Z}_4$inelevendimensionsandaD3-braneon${\mathbb C}^3/{\mathbb Z}_3$intendimensionshaveafamilyofblack$p$-branes on the orbifold ${\mathbb{C}}^n\mathrm{/}{\mathbb{Z}}_n$. These solutions are extremal and have regular horizons $S^{2n-1}\mathrm{/}{\mathbb{Z}}_n$ without any naked singularity, with near horizon geometries AdS${}_{p+2}\times S^{2n-1}\mathrm{/}{\mathbb{Z}}_n$.