Irrational cubic fourfolds with geometric K3 categories
For every sufficiently large admissible Hassett discriminant, we prove that a very general cubic fourfold of that discriminant is irrational, although its Kuznetsov component is equivalent to the ordinary derived category of a projective K3 surface. The discriminant threshold is ineffective. This disproves Kuznetsov's rationality conjecture. The same cubics have associated untwisted polarized K3 surfaces in the Hodge-theoretic sense, so they also disprove the sufficiency direction of the associated-K3 rationality prediction.
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— Shaowu Zhang (@ivanswzhang) Oct 11, 2026
— Shaowu Zhang (@ivanswzhang) Oct 12, 2026
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