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The regular quantizations of certain holomorphic bundles

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Abstract

In this paper, we study the regular quantizations of Kähler manifolds by using the first two coefficients of Bergman function expansions. Firstly, we obtain sufficient and necessary conditions for certain Hermitian holomorphic vector bundles and their ball subbundles to be regular quantizations. Secondly, we obtain that some projective bundles over the Fano manifolds M admit regular quantizations if and only if M are biholomorphically isomorphism to the complex projective spaces. Finally, we obtain the balanced metrics on certain Hermitian holomorphic vector bundles and their ball subbundles over the Riemann sphere.

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Change history

  • 27 January 2020

    The wrong funding number has been given in the acknowledgements section. It should be read: Nos. ZZ201818 and LZD014.

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Acknowledgements

The author would like to thank the referee for many helpful suggestions. The author was supported by the Scientific Research Fund of Leshan Normal University (No. ZZ201818).

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  1. School of Mathematical and Information Sciences, Leshan Normal University, Leshan, 614000, Sichuan, People’s Republic of China

    Zhiming Feng

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  1. Zhiming Feng
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Feng, Z. The regular quantizations of certain holomorphic bundles. Ann Glob Anal Geom 57, 95–120 (2020). https://doi.org/10.1007/s10455-019-09690-9

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  • DOI: https://doi.org/10.1007/s10455-019-09690-9

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