On Kähler surfaces of constant positive scalar curvature (Q1346082)

Let \(M\) be a compact complex 2-manifold which admits a Kähler metric for which the integral of the scalar curvature is positive. Suppose, moreover, that \(b_ 1(M) > 2\). Then if \(M\) is blown up at sufficiently many points, the resulting complex manifold \(\widetilde{M}\) admits Kähler metrics of constant positive scalar curvature.