We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection formalism as in the local family index theorem. To cite this article: X. Ma, W. Zhang, C. R. Acad. Sci. Paris, Ser. I 344 (2007). © 2006 Académie des sciences.
Ma, X., & Zhang, W. (2007). Superconnection and family Bergman kernels. Comptes Rendus Mathematique, 344(1), 41–44. https://doi.org/10.1016/j.crma.2006.11.013