On holomorphic tubular neighborhoods of compact Riemann surfaces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866917587268403200 |
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| author | Ogawa, Satoshi |
| author_facet | Ogawa, Satoshi |
| contents | We give a sufficient condition for the existence of a holomorphic tubular neighborhood of a compact Riemann surface holomorphically embedded in a non-singular complex surface. Our sufficient condition is described by an arithmetical condition of unitary flat line bundles which can be regarded as an analogue of the Brjuno condition for irrational numbers which appears in the theory of 1-variable complex dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07050 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On holomorphic tubular neighborhoods of compact Riemann surfaces Ogawa, Satoshi Complex Variables Dynamical Systems 37F50, 30F10, 57N40 We give a sufficient condition for the existence of a holomorphic tubular neighborhood of a compact Riemann surface holomorphically embedded in a non-singular complex surface. Our sufficient condition is described by an arithmetical condition of unitary flat line bundles which can be regarded as an analogue of the Brjuno condition for irrational numbers which appears in the theory of 1-variable complex dynamics. |
| title | On holomorphic tubular neighborhoods of compact Riemann surfaces |
| topic | Complex Variables Dynamical Systems 37F50, 30F10, 57N40 |
| url | https://arxiv.org/abs/2402.07050 |