Superconnection and family Bergman kernels

Superconnection and family Bergman kernels

We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem. Superconnexion et noyaux de Bergman en famille Résumé. Nous annonçons des résultats sur le développement asymptotique du noyau de Bergman en famille. Let W,S be smooth compact complex manifolds. Let π : W → S be a holomorphic submersion with comp...

Reproducing kernels , Bergman kernels , Poisson kernels

Weighted Bergman Kernels and Quantization

Let Ω be a bounded pseudoconvex domain in C N , φ, ψ two positive functions on Ω such that − logψ,− log φ are plurisubharmonic, z ∈ Ω a point at which − log φ is smooth and strictly plurisubharmonic, and M a nonnegative integer. We show that as k → ∞, the Bergman kernels with respect to the weights φkψM have an asymptotic expansion KφkψM (x, y) = kN πNφ(x, y)kψ(x, y)M ∞ ∑ j=0 bj(x, y) k −j , b0...

WEIGHTED BERGMAN KERNELS AND QUANTIZATIONMiroslav

Weighted Bergman kernels on orbifolds

We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line bundle.