Sextactic points on a simple closed curve

2000/08/17 by Gudlaugur Thorbergsson, Thorbergsson, Gudlaugur, Masaaki Umehara +1 · 2 citations
Computer Science · Mathematics · #51L15 #53A15 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Differential Geometry (math.DG) #FOS: Mathematics #Polynomial and algebraic computation #math.DG #msc:51L15 #msc:53A15

paper · pdf · doi:10.48550/arxiv.math/0008137

31pages, TeX

openalex publication_date 2000/08/17 · arxiv created 2000/12/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give optimal lower bounds for the number of sextactic points on a simple closed curve in the real projective plane. Sextactic points are after inflection points the simplest projectively invariant singularities on such curves. Our method is axiomatic and can be applied in other situations.

Cited by

• The Hesse pencil of plane curves and osculating conics
• Five-Point Hyperbolas on Power Curves and Near Lamé-Oval Vertices

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