Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2018
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| _version_ | 1866911948903284736 |
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| author | Marinescu, George Savale, Nikhil |
| author_facet | Marinescu, George Savale, Nikhil |
| contents | We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_00992 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface Marinescu, George Savale, Nikhil Differential Geometry Complex Variables Spectral Theory 53C17, 58J50, 32A25, 53D50 We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive line bundles whose curvature vanishes at finite order. The proof exploits the relation of the Bochner Laplacian on tensor powers with the sub-Riemannian (sR) Laplacian. |
| title | Bochner Laplacian and Bergman kernel expansion of semi-positive line bundles on a Riemann surface |
| topic | Differential Geometry Complex Variables Spectral Theory 53C17, 58J50, 32A25, 53D50 |
| url | https://arxiv.org/abs/1811.00992 |