Plane quartics and heptagons
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913483925225472 |
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| author | Agostini, Daniele Plaumann, Daniel Sinn, Rainer Wesner, Jannik Lennart |
| author_facet | Agostini, Daniele Plaumann, Daniel Sinn, Rainer Wesner, Jannik Lennart |
| contents | Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distinct complex heptagons. This number had been numerically computed by Kohn et al. We use intersection theory and the Scorza correspondence for quartics to show that 864 is an upper bound, complemented by a lower bound obtained through explicit analysis of the famous Klein quartic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_15759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Plane quartics and heptagons Agostini, Daniele Plaumann, Daniel Sinn, Rainer Wesner, Jannik Lennart Algebraic Geometry 14H50, 14H51, 52B99 Every polygon with n vertices in the complex projective plane is naturally associated with its adjoint curve of degree n-3. Hence the adjoint of a heptagon is a plane quartic. We prove that a general plane quartic is the adjoint of exactly 864 distinct complex heptagons. This number had been numerically computed by Kohn et al. We use intersection theory and the Scorza correspondence for quartics to show that 864 is an upper bound, complemented by a lower bound obtained through explicit analysis of the famous Klein quartic. |
| title | Plane quartics and heptagons |
| topic | Algebraic Geometry 14H50, 14H51, 52B99 |
| url | https://arxiv.org/abs/2408.15759 |