Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann-fock Model

@inproceedings{HEZARI2014AsymptoticEO,
  title={Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann-fock Model},
  author={HAMID HEZARI and CASEY KELLEHER and SHOO SETO and Xu Hang},
  year={2014}
}
  • HAMID HEZARI, CASEY KELLEHER, +1 author Xu Hang
  • Published 2014
We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated to the kth tensor powers of a positive line bundle L in a 1 √ k neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kähler potential kφ in a 1 √ k -neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann-Fock metric. We then prove that the Bergman kernel is also an asymptotic perturbation of the… CONTINUE READING