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MiS Preprint

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.

Mar 10, 2017
Mar 22, 2017
Real Algebraic Curves, Topology of Real Varieties, Computational Geometry

Related publications

2019 Repository Open Access
Nidhi Kaihnsa, Mario Kummer, Daniel Plaumann, Mahsa Sayyary Namin and Bernd Sturmfels

Sixty-four curves of degree six

In: Experimental mathematics, 28 (2019) 2, pp. 132-150