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Jun 7, 2023 at 11:25 comment added Gunnar Þór Magnússon @JasonStarr Thank you. I have actually read those. In the paper I'm looking for the authors worked with the standard local image of a blowup, and not that the first Hirzebruch surface can be realized as a projectivized bundle. I'm interested in their technique, not in the result itself.
Jun 7, 2023 at 11:06 comment added Jason Starr The article of Hitchin is the following: “On the curvature of rational surfaces”, in Differential geometry (Proc. Sympos. Pure Math., Vol. XXVII, Part 2, Stanford Univ., Stanford, 1973), American Mathematical Society, 1975, p.65-80.
Jun 7, 2023 at 11:04 comment added Jason Starr Actually, they attribute the result for Hirzebruch surfaces to Hitchin (they prove the result also for Hirzebruch manifolds of dimension greater than two).
Jun 7, 2023 at 11:03 comment added Jason Starr I do not know what article you read, but this is Theorem 1.3 in the following article, "Hirzebruch manifolds and positive holomorphic sectional curvature", by Bo Yang and Fangyang Zheng: numdam.org/item/10.5802/aif.3303.pdf
Jun 7, 2023 at 10:56 history asked Gunnar Þór Magnússon CC BY-SA 4.0