Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
Sixty-Four Curves of Degree Six
Nidhi Kaihnsa, Mario Denis Kummer, Daniel Plaumann, Mahsa Sayyary Namin and Bernd Sturmfels
We present a computational study of smooth curves of degree six in the real projective plane. The $56$ known combinatorial types are refined into $ 64$ rigid isotopy classes. Representative polynomials are constructed. Our classification software yields empirical probability distributions on the various types. Reality of the $324$ bitangents is studied. Lines that miss a given sextic form the avoidance locus. This is a union of up to $46$ convex regions, bounded by the dual curve. We also study the reality of inflection points, tensor eigenvectors, real tensor rank, and the construction of quartic surfaces.