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arXiv · 2607.26396

Twelve common flex lines in a general pencil of cubics

Jihao Liu·Yanze Wang
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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 Ro\'e. The main result of this paper was obtained using generative AI, particularly ChatGPT 5.5 Pro and the Danus system.

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Jihao Liu, Yanze Wang. 2026-07-29. Twelve common flex lines in a general pencil of cubics. https://arxiv.org/abs/2607.26396

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