Remark on the Off-Diagonal Expansion of the Bergman Kernel on Compact Kähler Manifolds

Abstract

In this short note, we compare our previous work on the off-diagonal expansion of the Bergman kernel and the preprint of Lu–Shiffman (arXiv:1301.2166). In particular, we note that the vanishing of the coefficient of p ^−1/2 is implicitly contained in Dai–Liu–Ma’s work (J. Differ. Geom. 72(1), 1–41, 2006) and was explicitly stated in our book (Holomorphic Morse inequalities and Bergman kernels. Progress in Math., vol. 254, 2007).

Keywords

Kähler manifold / Bergman kernel of a positive line bundle