Asymptotics of Bergman kernels

Abstract

We give an elementary proof of the existence of an asymptotic expansion in powers of $k$ of the Bergman kernel associated to $L^k$, where $L$ is a positive line bundle. We also give an algorithm for computing the coefficients in the expansion.

revised, mainly stylistic changes

References in corpus (1)

• Generalized Bergman kernels on symplectic manifolds

Cited by in corpus (6)

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• Limits of balanced metrics on vector bundles and polarised manifolds
• Bernstein polynomials, Bergman kernels and toric Kähler varieties
• Toeplitz Operators, Kähler Manifolds, and Line Bundles
• Geometry of Hermitian Algebraic Functions. Quotients of Squared Norms
• Berezin transform in polynomial Bergman spaces