Every projective manifold obtained from a toric manifold by finite point blow-ups admits a Kähler metric with positive holomorphic sectional curvature, completing the surface case of Yau's problem.
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Positive holomorphic sectional curvature on rational surfaces
Every projective manifold obtained from a toric manifold by finite point blow-ups admits a Kähler metric with positive holomorphic sectional curvature, completing the surface case of Yau's problem.