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

作者：Hezari Hamid; Kelleher Casey; Seto Shoo^*; Xu Hang

来源：Journal of Geometric Analysis, 2016, 26(4): 2602-2638.

DOI：10.1007/s12220-015-9641-3

• Bergman kernel
• Bargmann-Fock space
• Asymptotic expansion
• Kahler manifolds

We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated with the kth tensor powers of a positive line bundle L in a -neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kahler potential in a -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 Bargmann-Fock Bergman kernel.

• 出版日期2016-10