The first terms in the expansion of the Bergman kernel in higher degrees

Abstract

We establish the cancellation of the first $2j$ terms in the diagonal asymptotic expansion of the restriction to the $(0,2j)$-forms of the Bergman kernel associated to the spin${}^c$ Dirac operator on high tensor powers of a positive line bundle twisted by a (non necessarily holomorphic) complex vector bundle, over a compact Kähler manifold. Moreover, we give a local formula for the first and the second (non-zero) leading coefficients.

References in corpus (7)

• Generalized Bergman kernels on symplectic manifolds
• On the asymptotic expansion of Bergman kernel
• Berezin-Toeplitz quantization on Kaehler manifolds
• A closed formula for the asymptotic expansion of the Bergman kernel
• The SPIN${}^c$ Dirac operator on high tensor powers of a line bundle
• The first coefficients of the asymptotic expansion of the Bergman kernel of the spin^c Dirac operator
• Quantisation and the Hessian of Mabuchi energy

Cited by in corpus (1)

• The first terms in the expansion of the Bergman kernel in higher degrees: mixed curvature case