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MiS Preprint
23/2017

Sixty-Four Curves of Degree Six

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

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.

Received:
Mar 10, 2017
Published:
Mar 22, 2017
Keywords:
Real Algebraic Curves, Topology of Real Varieties, Computational Geometry

Related publications

inJournal
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