An application of Guillemin-Abreu theory to a non-abelian group action
  This note is a step towards demonstrating the benefits of a symplectic approach to studying equivariant K\"ahler geometry. We apply a local differential geometric framework from K\"ahler toric geometry due to Guillemin & Abreu to the case of the standard linear $\SU(n)$ action on $\bbC^n\setminus\{0\}$. Using this framework we (re)construct a scalar-flat K\"ahler metric on the blow-up of $\bbC^n$ at the origin from data on the moment polytope. 
Aleksis Raza