Sextactic and type-9 points on the Fermat cubic and associated objects

2024/06/19 by Łukasz Merta, Maciej Zięba, Merta, Łukasz +1 · 1 citation
Mathematics · #13A15 #14C20 #14N20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2406.13802

openalex publication_date 2024/06/19 · openalex created_date 2024/06/22 · openalex updated_date 2026/07/28

Abstract

In this note we study line and conic arrangements associated to sextactic and type 9 points on the Fermat cubic F and we provide explicit coordinates for each of the 72 type 9 points on F.

Cited by

• The Hesse pencil of plane curves and osculating conics

Related

• Sextactic points on the Fermat cubic curve and arrangements of conics
• The Fermat curves, arrangements of lines, and intersections of osculating curves
• On the configurations of nine points on a cubic curve
• Arrangements of inflectional lines, hyperosculating conics, and plane cubics
• Rational points on even dimensional Fermat cubics