Bergman Kernels on Symplectic Manifolds

Part of the Progress in Mathematics book series (PM, volume 254)


In this chapter, we study the asymptotic expansion of the Bergman kernel associated to modified Dirac operators and renormalized Bochner Laplacians on symplectic manifolds. We will also explain some applications of the asymptotic expansion in the symplectic case. One is, for example, the extension of the Berezin-Toeplitz quantization studied in Chapter 7. We also find Donaldson’s Hermitian scalar curvature as the second coefficient of the expansion.


Asymptotic Expansion Line Bundle Orthogonal Projection Dirac Operator Toeplitz Operator 
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