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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On projectivized vector bundles and positive holomorphic sectional curvature
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by Angelynn Alvarez, Gordon Heier and Fangyang Zheng
Proc. Amer. Math. Soc. 146 (2018), 2877-2882
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.
References
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Bibliographic Information
  • Angelynn Alvarez
  • Affiliation: Department of Mathematics, The State University of New York at Potsdam, 44 Pierrepont Avenue, Potsdam, New York 13676
  • MR Author ID: 1155523
  • Email: alvarear@potsdam.edu
  • Gordon Heier
  • Affiliation: Department of Mathematics, University of Houston, 4800 Calhoun Road, Houston, Texas 77204
  • MR Author ID: 697236
  • 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
  • MR Author ID: 272367
  • Email: zheng.31@osu.edu
  • 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
  • © Copyright 2018 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 146 (2018), 2877-2882
  • MSC (2010): Primary 32L05, 32Q10, 32Q15, 53C55
  • DOI: https://doi.org/10.1090/proc/13868
  • MathSciNet review: 3787350