Symplectic Non-hyperbolicity
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916691145916416 |
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| author | Cattalani, Spencer |
| author_facet | Cattalani, Spencer |
| contents | Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. We perform a systematic study based on their associated Ahlfors currents. In particular, we generalize (by a different method) a result of Bangert on the existence of complex lines. We show that Ahlfors currents control the asymptotic behavior of families of pseudoholomorphic curves, refining a result of Demailly. Lastly, we show that the space of Ahlfors currents is convex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_10790 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symplectic Non-hyperbolicity Cattalani, Spencer Symplectic Geometry Complex Variables Differential Geometry 32Q65, 32Q45, 53D35, 53C23 Complex (affine) lines are a major object of study in complex geometry, but their symplectic aspects are not well understood. We perform a systematic study based on their associated Ahlfors currents. In particular, we generalize (by a different method) a result of Bangert on the existence of complex lines. We show that Ahlfors currents control the asymptotic behavior of families of pseudoholomorphic curves, refining a result of Demailly. Lastly, we show that the space of Ahlfors currents is convex. |
| title | Symplectic Non-hyperbolicity |
| topic | Symplectic Geometry Complex Variables Differential Geometry 32Q65, 32Q45, 53D35, 53C23 |
| url | https://arxiv.org/abs/2504.10790 |