Generalized Bergman kernels on symplectic manifolds of bounded geometry
| Autor: | Xiaonan Ma, George Marinescu, Yuri A. Kordyukov |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Mathematics::Functional Analysis Mathematics::Complex Variables Applied Mathematics 010102 general mathematics Geometry 16. Peace & justice 01 natural sciences 010101 applied mathematics Line bundle Differential Geometry (math.DG) Bounded function Tensor (intrinsic definition) FOS: Mathematics Mathematics::Differential Geometry 0101 mathematics Mathematics::Symplectic Geometry Analysis Orbifold Symplectic geometry Mathematics Symplectic manifold Bergman kernel |
| DOI: | 10.48550/arxiv.1806.06401 |
| Popis: | We study the asymptotic behavior of the generalized Bergman kernel of the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a symplectic manifold of bounded geometry. First, we establish the off-diagonal exponential estimate for the generalized Bergman kernel. As an application, we obtain the relation between the generalized Bergman kernel on a Galois covering of a compact symplectic manifold and the generalized Bergman kernel on the base. Then we state the full off-diagonal asymptotic expansion of the generalized Bergman kernel, improving the remainder estimate known in the compact case to an exponential decay. Finally, we establish the theory of Berezin-Toeplitz quantization on symplectic orbifolds associated with the renormalized Bochner-Laplacian. Comment: 33 pages, v.2 is a final update to agree with the published paper |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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