Generalized Bergman kernels on symplectic manifolds
摘要
We study the near diagonal asymptotic expansion of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle over a compact symplectic manifold. We show how to compute the coefficients of the expansion by recurrence and give a closed formula for the first two of them. As consequence, we calculate the density of states function of the Bochner-Laplacian and establish a symplectic version of the convergence of the induced Fubini-Study metric. We also discuss generalizations of the asymptotic expansion for non-compact or singular manifolds as well as their applications. Our approach is inspired by the analytic localization techniques of Bismut-Lebeau.
引用
@article{arxiv.math/0411559,
title = {Generalized Bergman kernels on symplectic manifolds},
author = {Xiaonan Ma and George Marinescu},
journal= {arXiv preprint arXiv:math/0411559},
year = {2015}
}
备注
48 pages. Add two references on the Hermitian scalar curvature