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On projectivized vector bundles and positive holomorphic sectional curvature


Authors: Angelynn Alvarez, Gordon Heier and Fangyang Zheng
Journal: Proc. Amer. Math. Soc. 146 (2018), 2877-2882
MSC (2010): Primary 32L05, 32Q10, 32Q15, 53C55
DOI: https://doi.org/10.1090/proc/13868
Published electronically: March 30, 2018
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Abstract: We generalize a construction of Hitchin to prove that, given any compact Kähler manifold $ M$ with positive holomorphic sectional curvature and any holomorphic vector bundle $ E$ over $ M$, the projectivized vector bundle $ {\mathbb{P}}(E)$ admits a Kähler metric with positive holomorphic sectional curvature.


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Additional Information

Angelynn Alvarez
Affiliation: Department of Mathematics, The State University of New York at Potsdam, 44 Pierrepont Avenue, Potsdam, New York 13676
Email: alvarear@potsdam.edu

Gordon Heier
Affiliation: Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77204
Email: heier@math.uh.edu

Fangyang Zheng
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210 – and – Zhejiang Normal University, Jinhua, 321004, Zhejiang, People’s Republic of China
Email: zheng.31@osu.edu

DOI: https://doi.org/10.1090/proc/13868
Keywords: Compact complex manifolds, K\"ahler metrics, positive holomorphic sectional curvature, positive scalar curvature, projectivized vector bundles
Received by editor(s): June 29, 2016
Published electronically: March 30, 2018
Additional Notes: The third-named author was partially supported by a Simons Collaboration Grant
Communicated by: Lei Ni
Article copyright: © Copyright 2018 American Mathematical Society

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