Twelve common flex lines in a general pencil of cubics

2026/07/29 by Jihao Liu, Yanze Wang
Mathematics · #math.AG #msc:14H10 #msc:14H50 #msc:14N10

paper · pdf

9 pages. Mostly AI-generated, human-verified

arxiv created 2026/07/29 · arxiv updated 2026/07/30

Abstract

We prove that a general pencil of plane cubics over \mathbb C has exactly 12 common flex lines. This answers a question of Ciliberto, Miranda, and Roé. The main result of this paper was obtained using generative AI, particularly ChatGPT 5.5 Pro and the Danus system.

Citations

• Monodromy of projections of hypersurfaces

Related

• Pencils of Conic-Line Curves
• Pencils of cubics with eight base points lying in convex position in ℝP²
• Rational lines on smooth cubic surfaces
• Ideal of the variety of flexes of plane cubics
• Drawing cubic graphs with the four basic slopes