A symplectic dynamics proof of the degree-genus formula
We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere, defining the Hopf fibration. As an application, we prove the degree-genus formula for complex projective curves, using an elementary degeneration process inspired by the language of holomorphic bui...
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| Hauptverfasser: | , , |
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| Dokumenttyp: | Article (Journal) Kapitel/Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
8 May 2019
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| In: |
Arxiv
Year: 2019, Pages: 1-24 |
| DOI: | 10.48550/arXiv.1905.03054 |
| Online-Zugang: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.48550/arXiv.1905.03054 Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/1905.03054 
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| Verfasserangaben: | Peter Albers, Hansjörg Geiges, and Kai Zehmisch |
| Zusammenfassung: | We classify global surfaces of section for the Reeb flow of the standard contact form on the 3-sphere, defining the Hopf fibration. As an application, we prove the degree-genus formula for complex projective curves, using an elementary degeneration process inspired by the language of holomorphic buildings in symplectic field theory. |
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| Beschreibung: | Gesehen am 12.07.2022 |
| Beschreibung: | Online Resource |
| DOI: | 10.48550/arXiv.1905.03054 |