Scalar Curvature and Stability of Toric Fibrations

We study fibrations $\text{cV}$ of toric varieties over the flag variety $G\mathrm{/}T$, where $G$ is a compact semisimple Lie group and $T$ is a maximal torus. From symplectic data, we construct test configurations of $\text{cV}$ and compute their Futaki invariants by employing a generalization of Pick’s Theorem. We also give a simple form of the Mabuchi Functional.