Note on scalar curvature of extremal Kähler metrics on CP2#2CP2¯

In this note, we study scalar curvature of extremal Kähler metrics of CP2#2CP2¯. By the aid of computer algebra, we obtain the following result: Suppose that a Kähler class of CP2#2CP2¯ admits an extremal Kähler metric, and denote by Δa,bΔa,b the corresponding moment polygon of the Kähler class. Then the scalar curvature of the extremal Kähler metric will have a positive lower-bound max⁡{52,1ab}. Furthermore, if the moment polygon Δa,bΔa,b of the Kähler class satisfies the condition 12≤a,b<1, then the scalar curvature of the extremal Kähler metric have an upper-bound 9.