geometry-topology / Algebraic Geometry, Plane Curves

Twelve Common Flex Lines in a General Pencil of Cubics

Does a general pencil of plane cubics over $\mathbb{C}$ have exactly $12$ common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.

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geometry-topologyJul 29, 2026Significance 7/100Registry: unreviewed

Twelve Common Flex Lines in a General Pencil of Cubics

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Does a general pencil of plane cubics over $\mathbb{C}$ have exactly $12$ common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.

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Does a general pencil of plane cubics over $\mathbb{C}$ have exactly $12$ common flex lines? Ciliberto, Miranda and Roé asked this in Remark 5.3 of their paper; the answer is yes.

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