  We search for Ricci flat, K\"{a}hler geometries which are asymptotic to the
cone whose base is the space T^{11} by working out covariantly constant spinor
equations. The metrics we find are singular in the interior and introducing
parallel D3-branes does not form regular event horizons cloaking the naked
singularities. We also work out a supersymmetric ansatz involving only the
metric and the 5-form field corresponding to D3-branes wrapping over the
non-trivial 2-cycle of T^{11}. We find a system of first-order equations and
argue that the solution has an event horizon and the ADM mass per unit volume
diverges logarithmically.
