2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/97176This article finds constant scalar curvature Kahler metrics on certain compact complex surfaces. The surfaces considered are those admitting a holomorphic submersion to a curve, with fibres of genus at least 2. The proof is via an adiabatic limit. An approximate solution is constructed out of the hyperbolic metrics on the fibres and a large multiple of a certain metric on the base. A parameter-dependent inverse function theorem is then used to perturb the approximate solution to a genuine solution in the same cohomology class. The arguments also apply to certain higher dimensional fibred Kahler manifolds.32 pages, no figures (with minor corrections and a larger font for tired eyes)Differential Geometrytext