Sixty-Four Curves of Degree Six

Nidhi Kaihnsa, Mario Denis Kummer, Daniel Plaumann, Mahsa Sayyary Namin, and Bernd Sturmfels

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Submission date: 10. Mar. 2017 (revised version: July 2017)
Pages: 31
published in: Experimental mathematics, 28 (2019) 2, p. 132-150 
DOI number (of the published article): 10.1080/10586458.2017.1360808
Bibtex
Keywords and phrases: Real Algebraic Curves, Topology of Real Varieties, Computational Geometry
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Abstract:
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.