English

The regular quantizations of certain holomorphic bundles

Complex Variables 2019-09-30 v1

Abstract

In this paper, we study the regular quantizations of K\"{a}hler 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 MM admit regular quantizations if and only if MM 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.

Keywords

Cite

@article{arxiv.1909.12629,
  title  = {The regular quantizations of certain holomorphic bundles},
  author = {Zhiming Feng},
  journal= {arXiv preprint arXiv:1909.12629},
  year   = {2019}
}
R2 v1 2026-06-23T11:28:02.768Z