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On projectivized vector bundles and positive holomorphic sectional curvature
Angelynn Alvarez, Gordon Heier, Fangyang Zheng
Source abstract
We generalize a construction of Hitchin to prove that, given any compact Kähler manifold M M with positive holomorphic sectional curvature and any holomorphic vector bundle E E over M M , the projectivized vector bundle P ( E ) {\mathbb P}(E) admits a Kähler metric with positive holomorphic sectional curvature.
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