A note on the Bergman kernel. (Sur le noyau de Bergman.) (English. French summary) Zbl 1308.32005
Summary: It is known that the Bergman kernel associated with \(L^{k}\), where \(L\) is positive line bundle over a complex compact manifold, has an asymptotic expansion. We give an elementary proof of the fact that the subprincipal term of this expansion is the scalar curvature.
MSC:
| 32A25 | Integral representations; canonical kernels (Szegő, Bergman, etc.) |
| 32L05 | Holomorphic bundles and generalizations |
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