121 Patchworked Curves of Degree Seven
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910029747060736 |
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| author | Geiselmann, Zoe Joswig, Michael Kastner, Lars Mundinger, Konrad Pokutta, Sebastian Spiegel, Christoph Wack, Marcel Zimmer, Max |
| author_facet | Geiselmann, Zoe Joswig, Michael Kastner, Lars Mundinger, Konrad Pokutta, Sebastian Spiegel, Christoph Wack, Marcel Zimmer, Max |
| contents | The 121 real schemes, i.e., ambient isotopy classes, of smooth real plane algebraic curves of degree seven were classified by Viro (1984). By constructing one patchwork of the dilated triangle $7\cdotΔ_2$ for each real scheme, we provide an explicit method for constructing polynomials realizing each real scheme. In particular, every real scheme of degree seven can be realized as a T-curve; this settles a question raised by Itenberg and Viro (1996). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_06888 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | 121 Patchworked Curves of Degree Seven Geiselmann, Zoe Joswig, Michael Kastner, Lars Mundinger, Konrad Pokutta, Sebastian Spiegel, Christoph Wack, Marcel Zimmer, Max Algebraic Geometry Combinatorics 14P25 (14H50, 14T15, 52B20, 57Q37) The 121 real schemes, i.e., ambient isotopy classes, of smooth real plane algebraic curves of degree seven were classified by Viro (1984). By constructing one patchwork of the dilated triangle $7\cdotΔ_2$ for each real scheme, we provide an explicit method for constructing polynomials realizing each real scheme. In particular, every real scheme of degree seven can be realized as a T-curve; this settles a question raised by Itenberg and Viro (1996). |
| title | 121 Patchworked Curves of Degree Seven |
| topic | Algebraic Geometry Combinatorics 14P25 (14H50, 14T15, 52B20, 57Q37) |
| url | https://arxiv.org/abs/2602.06888 |