Abstract
LetM be a compact complex 2-manifold that admits a Kähler metric for which the integral of the scalar curvature is positive. Suppose, moreover, that b1 (M) > 2. Then, ifM is blown up at sufficiently many points, the resulting complex manifold ~M admits Kähler metrics of constant positive scalar curvature.
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C.L. supported in part by NSF Grant DMS 90-03263.
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LeBrun, C., Simanca, S.R. On Kähler surfaces of constant positive scalar curvature. J Geom Anal 5, 115–127 (1995). https://doi.org/10.1007/BF02926444
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DOI: https://doi.org/10.1007/BF02926444