Constant Scalar Curvature of Toric Fibrations

We study the conditions under which a fibration of toric varieties, fibered over a flag variety, admits a constant scalar curvature Kahler metric. We first provide an introduction to toric varieties and toric fibrations and derive the scalar curvature equation. Next we derive interior a priori estimates of all orders and a global Linfinity-estimate for the scalar curvature equation. Finally we extend the theory of K-Stability to this setting and construct test-configurations for these spaces.