Relative K-polystability of projective bundles over a curve
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- by Vestislav Apostolov and Julien Keller PDF
- Trans. Amer. Math. Soc. 372 (2019), 233-266 Request permission
Abstract:
Let $\mathbb {P}(E)$ be the projectivization of a holomorphic vector bundle $E$ over a compact complex curve $C$. We characterize the existence of an extremal Kähler metric on $\mathbb {P}(E)$ in terms of relative K-polystability and the fact that $E$ decomposes as a direct sum of stable bundles.References
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Additional Information
- Vestislav Apostolov
- Affiliation: Département de Mathématiques, UQAM, C.P. 8888 Succ. Centre-ville, Montréal, Québec H3C 3P8, Canada
- MR Author ID: 772555
- Email: apostolov.vestislav@uqam.ca
- Julien Keller
- Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, Institut de Mathématiques de Marseille, UMR 7373, 13453 Marseille, France
- MR Author ID: 366272
- Email: julien.keller@univ-amu.fr
- Received by editor(s): April 26, 2017
- Received by editor(s) in revised form: February 20, 2018
- Published electronically: March 25, 2019
- Additional Notes: The first author was supported in part by an NSERC Discovery grant. He is grateful to the University Aix-Marseille and to the Institute of Mathematics and Informatics of the Bulgarian Academy of Science for their hospitality and support during the preparation of this work.
The second author’s work was carried out in the framework of the Labex Archimède (ANR-11-LABX-0033) and of the A*MIDEX project (ANR-11-IDEX-0001-02), funded by the “Investissements d’Avenir” French government programme managed by the French National Research Agency (ANR). He was also partially supported by the ANR project EMARKS, decision No. ANR-14-CE25-0010. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 233-266
- MSC (2010): Primary 14L24; Secondary 58E11, 32Q15, 14H60, 53C07
- DOI: https://doi.org/10.1090/tran/7556
- MathSciNet review: 3968768