Generalized Bergman kernels on symplectic manifolds
| Autor: | Xiaonan Ma, George Marinescu |
|---|---|
| Rok vydání: | 2004 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics(all) Pure mathematics General Mathematics Symplectic manifold Line bundle Tensor (intrinsic definition) FOS: Mathematics Tensor Complex Variables (math.CV) Symplectomorphism Moment map Mathematics::Symplectic Geometry Mathematics Bergman kernel Mathematics - Complex Variables Mathematical analysis General Medicine Generalized Bergman kernel Differential Geometry (math.DG) Mathematics - Symplectic Geometry Symplectic Geometry (math.SG) 58Jxx 53Dxx Mathematics::Differential Geometry Asymptotic expansion Symplectic geometry |
| Zdroj: | Comptes Rendus Mathematique. 339:493-498 |
| ISSN: | 1631-073X |
| Popis: | 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. 48 pages. Add two references on the Hermitian scalar curvature |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|