Greatest lower bounds on the Ricci curvature of Fano manifolds

On a Fano manifold M we study the supremum of the possible t such that there is a K"ahler metric in c_1(M) with Ricci curvature bounded below by t. This is shown to be the same as the maximum existence time of Aubin’s continuity path for finding K"ahler-Einstein metrics. We show that on P^2 blown up in one point this supremum is 6/7, and we give upper bounds for other manifolds.