Berndtsson-Lempert-Szőke Fields Associated to Proper Holomorphic Families of Vector Bundles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914746609958912 |
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| author | Varolin, Dror |
| author_facet | Varolin, Dror |
| contents | Drawing on work of Berndtsson and of Lempert and Szőke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but nevertheless have a reasonable definition of curvature that agrees with the curvature of the Chern connection when the family of Hilbert spaces is locally trivial. We thus obtain a new proof of a celebrated theorem of Berndtsson on the curvature of direct images of semi-positively twisted relative canonical bundles (i.e., adjoint bundles), and of its higher-rank generalization due to Liu and Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_12802 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Berndtsson-Lempert-Szőke Fields Associated to Proper Holomorphic Families of Vector Bundles Varolin, Dror Complex Variables Algebraic Geometry Differential Geometry Drawing on work of Berndtsson and of Lempert and Szőke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but nevertheless have a reasonable definition of curvature that agrees with the curvature of the Chern connection when the family of Hilbert spaces is locally trivial. We thus obtain a new proof of a celebrated theorem of Berndtsson on the curvature of direct images of semi-positively twisted relative canonical bundles (i.e., adjoint bundles), and of its higher-rank generalization due to Liu and Yang. |
| title | Berndtsson-Lempert-Szőke Fields Associated to Proper Holomorphic Families of Vector Bundles |
| topic | Complex Variables Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2201.12802 |