A symplectic construction of Calabi's extremal K\"ahler metrics on the   blow-up of $\bbC\bbP^n$ at one point
  We apply a local differential geometric framework from K\"ahler toric geometry to (re)construct Calabi's extremal K\"ahler metrics on $\bbC\bbP^n$ blown-up at a point from data on the moment polytope. 
Aleksis Raza