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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math.DG 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Uniform weak RC-positivity of TX on a compact Kähler manifold X implies X is projective and rationally connected; the same condition on any holomorphic vector bundle E yields a Hermitian metric with positive mean curvature.
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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.
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Uniform weak RC-positivity and rational connectedness
Uniform weak RC-positivity of TX on a compact Kähler manifold X implies X is projective and rationally connected; the same condition on any holomorphic vector bundle E yields a Hermitian metric with positive mean curvature.