Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909536955138048 |
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| author | Ebenfelt, Peter Ganguly, Soumya Xiao, Ming |
| author_facet | Ebenfelt, Peter Ganguly, Soumya Xiao, Ming |
| contents | On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the Bergman kernel. As an application, we characterize two dimensional ball quotients as the only Stein spaces with smooth finite type boundary and locally rational Bergman kernel. A key ingredient in the proof of the degree estimate is a new localization result for the Bergman kernel of a pseudoconvex, finite type domain in a complex manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13989 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries Ebenfelt, Peter Ganguly, Soumya Xiao, Ming Complex Variables 32E10, 32C20, 32Q57, 32T25 On a two dimensional Stein space with isolated, normal singularities, smooth finite type boundary, and locally algebraic Bergman kernel, we establish an estimate on the type of the boundary in terms of the local algebraic degree of the Bergman kernel. As an application, we characterize two dimensional ball quotients as the only Stein spaces with smooth finite type boundary and locally rational Bergman kernel. A key ingredient in the proof of the degree estimate is a new localization result for the Bergman kernel of a pseudoconvex, finite type domain in a complex manifold. |
| title | Local algebraicity and localization of the Bergman kernel on Stein spaces with finite type boundaries |
| topic | Complex Variables 32E10, 32C20, 32Q57, 32T25 |
| url | https://arxiv.org/abs/2408.13989 |