Asymptotic Expansion of the Bergman Kernel via Perturbation of the Bargmann–Fock Model
| Autor: | Hamid Hezari, Shoo Seto, Hang Xu, Casey Lynn Kelleher |
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| Rok vydání: | 2015 |
| Předmět: |
Mathematics::Functional Analysis
Mathematics::Complex Variables 010308 nuclear & particles physics 010102 general mathematics Diagonal Mathematical analysis Perturbation (astronomy) 01 natural sciences Fock space symbols.namesake Differential geometry Line bundle Fourier analysis 0103 physical sciences symbols Geometry and Topology 0101 mathematics Asymptotic expansion Mathematical physics Mathematics Bergman kernel |
| Zdroj: | The Journal of Geometric Analysis. 26:2602-2638 |
| ISSN: | 1559-002X 1050-6926 |
| DOI: | 10.1007/s12220-015-9641-3 |
| Popis: | We give an alternate proof of the existence of the asymptotic expansion of the Bergman kernel associated with the kth tensor powers of a positive line bundle L in a \(\frac{1}{\sqrt{k}}\)-neighborhood of the diagonal using elementary methods. We use the observation that after rescaling the Kahler potential \(k\varphi \) in a \(\frac{1}{\sqrt{k}}\)-neighborhood of a given point, the potential becomes an asymptotic perturbation of the Bargmann–Fock metric. We then prove that the Bergman kernel is also an asymptotic perturbation of the Bargmann–Fock Bergman kernel. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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