Abstract: Let $X \to \mathbb{P}^N$ be a smooth linearly normal projective variety, and $(R_X, \Delta_X)$ the pair of Chow/Hurwitz forms. It was proved by S. Paul that the K-energy of $X$ restricted to the Bergman metrics is bounded from below if and only if the pair $(R_X, \Delta_X)$ is semistable. In this talk, for a smooth projective toric variety $X$ and a positive integer i>0, we give a necessary and sufficient condition for the pair $(R_X, \Delta_X)$ to be semistable with respect to O_X(i), using the theory of Gelfand-Kapranov-Zelevinsky (A-Resultants/A-Discriminants).
