On conifolds and D3-branes

We search for Ricci flat, Kähler geometries which are asymptotic to the cone whose base is the space T11 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 nontrivial 2-cycle of T11. 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.