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
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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