Ziegler's nonfreeness conjecture for generic cuts of free arrangements

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Let A′{\mathcal{A}}' be an essential and free arrangement in Kℓ{\mathbb{K}}^\ell with ℓ≥4\ell\geq4, let XX be a generic subspace with dim⁡X>2\dim X>2, and let A′∩X{\mathcal{A}}'\cap X be the restriction defined by

A′∩X={H∩X∣H∈A′∖AX′}.{\mathcal{A}}'\cap X=\{H\cap X\mid H\in{\mathcal{A}}'\setminus{\mathcal{A}}'_X\}.

Ziegler's nonfreeness conjecture. For A′{\mathcal{A}}' and XX as in Ziegler's generic restriction conjecture, the arrangement A′∩X{\mathcal{A}}'\cap X is never free; equivalently, a generic cut of a free arrangement is not free. The source presents this as an implication Ziegler said would follow if the preceding conjecture were true; no resolution is given.

References

Primary source

Takuro Abe and Graham Denham, “On Ziegler's conjectures for logarithmic derivations of arrangements”, arXiv:2307.08173 (2026).

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