We classify all 121 real schemes of smooth real plane algebraic curves of degree seven by constructing patchworks. We provide an explicit method for constructing polynomials realizing each real scheme. The work demonstrates that every real scheme at this degree level can be realized as a T-curve, resolving a previously open question from 1996.
@article{geiselmann2026patchworked,title={121 Patchworked Curves of Degree Seven},author={Geiselmann, Zoe and Joswig, Michael and Kastner, Lars and Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Wack, Marcel and Zimmer, Max},journal={arXiv preprint arXiv:2602.06888},year={2026},}
