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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Criteria for the ampleness of certain vector bundles
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by Indranil Biswas and Vamsi Pritham Pingali
Proc. Amer. Math. Soc. 152 (2024), 1961-1968
DOI: https://doi.org/10.1090/proc/16721
Published electronically: March 27, 2024

Abstract:

We prove that certain vector bundles over surfaces are ample if they are so when restricted to divisors, certain numerical criteria hold, and they are semistable (with respect to $\det (E)$). This result is a higher-rank version of a theorem of Schneider and Tancredi for vector bundles of rank two over surfaces. We also provide counterexamples indicating that our theorem is sharp.
References
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Bibliographic Information
  • Indranil Biswas
  • Affiliation: Department of Mathematics, Shiv Nadar University, NH91, Tehsil Dadri, Greater Noida, Uttar Pradesh 201314, India
  • MR Author ID: 340073
  • Email: indranil.biswas@snu.edu.in, indranil29@gmail.com
  • Vamsi Pritham Pingali
  • Affiliation: Department of Mathematics, Indian Institute of Science, Bangalore 560012, India
  • MR Author ID: 1049748
  • Email: vamsipingali@iisc.ac.in
  • Received by editor(s): October 24, 2022
  • Received by editor(s) in revised form: April 30, 2023, July 30, 2023, and November 6, 2023
  • Published electronically: March 27, 2024
  • Additional Notes: The first author was partially supported by the J. C. Bose Fellowship (JBR/2023/000003).
    The second author was partially supported by the DST FIST program - 2021 (TPN - 700661).
  • Communicated by: Filippo Bracci
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 1961-1968
  • MSC (2020): Primary 14J60, 14F17, 32L10
  • DOI: https://doi.org/10.1090/proc/16721
  • MathSciNet review: 4728466