Remark on the off-diagonal expansion of the Bergman kernel on compact Kähler manifolds

Xiaonan Ma (1) , George Marinescu (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 Mathematisches Institut

In this short note, we compare our previous works on the off-diagonal expansion of the Bergman kernel and the recent 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. Differential Geom. 72 (2006), no. 1, 1-41) and was explicitly stated in our book (Holomorphic Morse inequalities and Bergman kernels, Progress in Math., vol. 254, Birkhäuser, 2007).

Domaines: Géométrie différentielle [math.DG]; Variables complexes [math.CV]

Xiaonan Ma, George Marinescu. Remark on the off-diagonal expansion of the Bergman kernel on compact Kähler manifolds. 2013. ⟨hal-00872361⟩