Geometric quantization results for semi-positive line bundles on a Riemann surface
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866909148730359808 |
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| author | Marinescu, George Savale, Nikhil |
| author_facet | Marinescu, George Savale, Nikhil |
| contents | In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the expansion in the semipositive case including: Tian's approximation theorem for induced Fubini-Study metrics, leading order asymptotics and composition for Toeplitz operators, asymptotics of zeroes for random sections and the asymptotics of holomorphic torsion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14372 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Geometric quantization results for semi-positive line bundles on a Riemann surface Marinescu, George Savale, Nikhil Differential Geometry Mathematical Physics Complex Variables Probability In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the expansion in the semipositive case including: Tian's approximation theorem for induced Fubini-Study metrics, leading order asymptotics and composition for Toeplitz operators, asymptotics of zeroes for random sections and the asymptotics of holomorphic torsion. |
| title | Geometric quantization results for semi-positive line bundles on a Riemann surface |
| topic | Differential Geometry Mathematical Physics Complex Variables Probability |
| url | https://arxiv.org/abs/2310.14372 |