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.
Cite
@misc{OAI:Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026,
author = {{OpenAI}},
title = {{Irrational cubic fourfolds with geometric K3 categories}},
howpublished = {OpenAI Math Release preprint
\href{https://github.com/openai/math/blob/main/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026.pdf}{OAI:Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026}},
year = {2026}
}