Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910595209494528 |
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| author | Hashimoto, Yoshinori Koike, Takayuki Matsumura, Shin-ichi |
| author_facet | Hashimoto, Yoshinori Koike, Takayuki Matsumura, Shin-ichi |
| contents | In this paper, we extend the uniform $L^2$-estimate of $\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact Kähler manifolds in the previous work, to compact complex manifolds. In the proof, by tracing the Dolbeault isomorphism in detail, we derive the desired $L^2$-estimate directly from Ueda's lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05300 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds Hashimoto, Yoshinori Koike, Takayuki Matsumura, Shin-ichi Complex Variables 32W05 (Primary), 53C07 (Secondary) In this paper, we extend the uniform $L^2$-estimate of $\bar{\partial}$-equations for flat nontrivial line bundles, proved for compact Kähler manifolds in the previous work, to compact complex manifolds. In the proof, by tracing the Dolbeault isomorphism in detail, we derive the desired $L^2$-estimate directly from Ueda's lemma. |
| title | Uniform $L^2$-estimates for flat nontrivial line bundles on compact complex manifolds |
| topic | Complex Variables 32W05 (Primary), 53C07 (Secondary) |
| url | https://arxiv.org/abs/2409.05300 |