Kähler surfaces of positive scalar curvature (Q1381945)

The author constructs Kähler metrics of positive scalar curvature on the ruled surfaces obtained by blowing-up distinct points on a minimal model. These ruled surfaces are generic in the sense that any ruled surface is contained in a semi-universal family whose general member is of this type. These results are analogous to those obtained by \textit{N. J. Hitchin} [Proc. Symp. Pure Math. 27, 65-80 (1975; Zbl 0321.53052)] for rational surfaces and the proofs use Hitchin's methods. One can summarise by saying that there exist Kähler metrics of positive scalar curvature on almost all rational and ruled surfaces.