# The Gibbons-Hawking ansatz over a wedge

## TL;DR

This paper studies Ricci-flat metrics with cone singularities on complex 2-space, analyzing their asymptotic behavior and energy, based on Donaldson's construction using the Gibbons-Hawking ansatz over wedges.

## Contribution

It provides a detailed description of the asymptotics and energy computations for Donaldson's Ricci-flat cone singularity metrics using the Gibbons-Hawking ansatz.

## Key findings

- Describes asymptotic behavior at infinity.
- Computes the energy of the metrics.
- Analyzes the structure of cone singularities.

## Abstract

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.