Explicit self-dual metrics on CP₂#⋯#CP₂

We display explicit half-conformally-flat metrics on the connected sum of any number of copies of the complex projective plane. These metrics are obtained from magnetic monopoles in hyperbolic 3-space by an analogue of the Gibbons-Hawking ansatz, and are conformal compactifications of asymptotically-flat, scalar-flat Kahler metrics on n-fold blow-ups of C². The corresponding twistor spaces are also displayed explicitly, and are observed to be Moishezon manifolds— that is, they are bimeromor-phic to projective varieties.