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

Abstract

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).

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

References in corpus (1)

• The SPIN${}^c$ Dirac operator on high tensor powers of a line bundle

Cited by in corpus (10)

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• Berezin-Toeplitz quantization for lower energy forms
• On the full asymptotic of analytic torsion
• On the composition of Berezin-Toeplitz operators on symplectic manifolds
• The growth of dimension of cohomology of semipositive line bundles on Hermitian manifolds
• The first terms in the expansion of the Bergman kernel in higher degrees
• CR eigenvalue estimate and Kohn-Rossi cohomology