Ohta, Hiroshi; Ono, Kaoru Notes on symplectic 4-manifolds with \(b_ 2^ + = 1\). II. (English) Zbl 0873.53020 Int. J. Math. 7, No. 6, 755-770 (1996). [For part I, see the preceding review Zbl 0873.53019.]The authors apply the Taubes Theorems [C. H. Taubes, Math. Res. Lett. 1, 809-822 (1994; Zbl 0853.57019); Math. Res. Lett. 2, 9-13 (1995; Zbl 0854.57019); Math. Res. Lett. 2, 221-238 (1995; Zbl 0854.57020); J. Am. Math. Soc. 9, 845-918 (1996; Zbl 0867.53025)] to study closed smooth 4-manifolds \(X\) having a symplectic structure and a metric of positive scalar curvature. The main result of the paper states that such an \(X\) must be diffeomorphic to either the complex projective plane or a ruled surface up to blow-up and down. In particular, if \(c_1(K^{-1}_X)= \lambda[\omega]\) with a positive number \(\lambda\), then \(X\) must be diffeomorphic to a Del Pezzo surface.[See also the following review Zbl 0873.53021]. Reviewer: A.Cavicchioli (Modena) Cited in 3 ReviewsCited in 18 Documents MSC: 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.) Keywords:4-manifolds; symplectic structure; positive scalar curvature; ruled surface Citations:Zbl 0873.53019; Zbl 0853.57019; Zbl 0854.57019; Zbl 0854.57020; Zbl 0867.53025; Zbl 0873.53021 PDFBibTeX XMLCite \textit{H. Ohta} and \textit{K. Ono}, Int. J. Math. 7, No. 6, 755--770 (1996; Zbl 0873.53020) Full Text: DOI