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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/2503.10564 |
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| _version_ | 1866912547049832448 |
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| author | Benoist, Olivier Wittenberg, Olivier |
| author_facet | Benoist, Olivier Wittenberg, Olivier |
| contents | We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can be applied in particular when the target is a smooth hypersurface of degree d in P^n with n greater than or equal to d^2-1. We deduce it from a more general result: the tight approximation property holds for rationally simply connected varieties over function fields of complex curves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_10564 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tight approximation for rationally simply connected varieties Benoist, Olivier Wittenberg, Olivier Algebraic Geometry Complex Variables We prove that holomorphic maps from an open subset of a complex smooth projective curve to a complex smooth projective rationally simply connected variety can be approximated by algebraic maps for the compact-open topology. This theorem can be applied in particular when the target is a smooth hypersurface of degree d in P^n with n greater than or equal to d^2-1. We deduce it from a more general result: the tight approximation property holds for rationally simply connected varieties over function fields of complex curves. |
| title | Tight approximation for rationally simply connected varieties |
| topic | Algebraic Geometry Complex Variables |
| url | https://arxiv.org/abs/2503.10564 |