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

The recent discovery of an explicit solution of a black hole on the resolved orbifold ${\mathbb C}^n/{\mathbb Z}_n$ 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 ${\mathbb C}^4/{\mathbb Z}_4$ in eleven dimensions and a D3-brane on ${\mathbb C}^3/{\mathbb Z}_3$ in ten dimensions have a family of black $p$-branes on the orbifold ${\mathbb C}^n/{\mathbb Z}_n$. These solutions are extremal and have regular horizons $S^{2n-1}/{\mathbb Z}_n$ without any naked singularity, with near horizon geometries AdS${}_{p+2}\times S^{2n-1}/{\mathbb Z}_n$.

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