The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator

Details The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator

2005-11-16

arxiv.org/abs/math/0511395v2

Mathematics

Complex Variables

21 pages, to appear in Internat. J. Math. Precisions added in the abstract

Scientific paper

We establish the existence of the asymptotic expansion of the Bergman kernel associated to the spin-c Dirac operators acting on high tensor powers of line bundles with non-degenerate mixed curvature (negative and positive eigenvalues) by extending the paper " On the asymptotic expansion of Bergman kernel " (math.DG/0404494) of Dai-Liu-Ma. We compute the second coefficient b_1 in the asymptotic expansion using the method of our paper "Generalized Bergman kernels on symplectic manifolds" (math.DG/0411559).

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