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I present a construction of real or complex selfdual conformal 4-manifolds(of signature (2,2) in the real case) from a natural gauge field equation on areal or complex projective surface, the gauge group being the group ofdiffeomorphisms of a real or complex 2-manifold. The 4-manifolds obtained arecharacterized by the existence of a foliation by selfdual null surfaces of aspecial kind. The classification by Dunajski and West of selfdual conformal4-manifolds with a null conformal vector field is the special case in which thegauge group reduces to the group of diffeomorphisms commuting with a vectorfield, and I analyse the presence of compatible scalar-flat K\"ahler,hypercomplex and hyperk\"ahler structures from a gauge-theoretic point of view.In an appendix, I discuss the twistor theory of projective surfaces, which isused in the body of the paper, but is also of independent interest.Comment: for Progress in Twistor Theory, SIGM

Selfdual 4-Manifolds, Projective Surfaces, and the Dunajski-West Construction