Abstract
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.
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8.4 Bibliographic notes
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(2007). Bergman Kernels on Symplectic Manifolds. In: Holomorphic Morse Inequalities and Bergman Kernels. Progress in Mathematics, vol 254. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8115-8_9
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DOI: https://doi.org/10.1007/978-3-7643-8115-8_9
Publisher Name: Birkhäuser Basel
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