The Gibbons-Hawking ansatz over a wedge

We discuss the Ricci-flat `model metrics’ on ${\mathbb{C}}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in ${\mathbb{R}}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.