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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.12211 |
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| _version_ | 1866909905290526720 |
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| author | Shen, Shu Yu, Jianqing |
| author_facet | Shen, Shu Yu, Jianqing |
| contents | We give a new differential-geometric proof of Grauert's theorem on the coherence of the higher direct image of a coherent sheaf under a proper holomorphic morphism between complex analytic spaces. In the smooth case, our approach is based on the antiholomorphic superconnection introduced by Block and further developed by Bismut-Shen-Wei. The required finiteness results follow from elliptic theory. In the singular case, we reduce the problem to the smooth setting using Hironaka's desingularization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12211 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Grauert's direct image theorem via superconnections and desingularizations Shen, Shu Yu, Jianqing Algebraic Geometry Complex Variables Differential Geometry 14F08, 18G80, 58J10, 35J05, 32S45 We give a new differential-geometric proof of Grauert's theorem on the coherence of the higher direct image of a coherent sheaf under a proper holomorphic morphism between complex analytic spaces. In the smooth case, our approach is based on the antiholomorphic superconnection introduced by Block and further developed by Bismut-Shen-Wei. The required finiteness results follow from elliptic theory. In the singular case, we reduce the problem to the smooth setting using Hironaka's desingularization. |
| title | Grauert's direct image theorem via superconnections and desingularizations |
| topic | Algebraic Geometry Complex Variables Differential Geometry 14F08, 18G80, 58J10, 35J05, 32S45 |
| url | https://arxiv.org/abs/2511.12211 |