Abstract
We construct Kähler metrics of positive scalar curvature on almost all blown-up ruled surfaces of arbitrary genus. The metrics have an explicit form on ruled surfaces blown up at most twice successively from a minimal model. Our surfaces are generic in the sense that they make up a dense set in the deformations of a given ruled surface.
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Sung, MH. Kähler Surfaces of Positive Scalar Curvature. Annals of Global Analysis and Geometry 15, 509–518 (1997). https://doi.org/10.1023/A:1006543703319
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DOI: https://doi.org/10.1023/A:1006543703319