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THE FIRST COEFFICIENTS OF THE ASYMPTOTIC EXPANSION OF THE BERGMAN KERNEL OF THE Spin c DIRAC OPERATOR

2006; World Scientific; Volume: 17; Issue: 06 Linguagem: Inglês

10.1142/s0129167x06003667

ISSN

1793-6519

Autores

Xiaonan Ma, George Marinescu,

Tópico(s)

Geometric Analysis and Curvature Flows

Resumo

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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