Kuznetsov's rationality conjecture for cubic fourfolds
Claims that for every sufficiently large admissible Hassett discriminant a very general cubic fourfold of discriminant is irrational although its Kuznetsov component is the derived category of a K3 surface and it has an associated polarized K3 in Hassett's Hodge-theoretic sense. This disproves Kuznetsov's conjecture and the sufficiency of the associated-K3 criterion (and of Fano variety birational to a K3 Hilbert square). The threshold is ineffective; no specific discriminant is shown irrational, the necessity direction is untouched, and stable rationality is not decided. These are not the first irrational cubic fourfolds: the paper cites Katzarkov-Kontsevich-Pantev-Yu (very general cubic) and Fay (some special divisors).
Exact FrontierDelta
Scope and record
Occurred: Sep 24, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Kuznetsov's rationality conjecture for cubic fourfolds · Kuznetsov's conjecture on cubic fourfolds
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
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VibeMathed
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Unreleased internal OpenAI model
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Kuznetsov's rationality conjecture for cubic fourfolds parent of this event
Kuznetsov's rationality conjecture for cubic fourfolds evidence for this event
This event attributed to Unreleased internal OpenAI model
VibeMathed record: Kuznetsov's rationality conjecture for cubic fourfolds evidence for this event
Claims that for every sufficiently large admissible Hassett discriminant a very general cubic fourfold of discriminant is irrational although its Kuznetsov component is the derived category of a K3 surface and it has an associated polarized K3 in Hassett's Hodge-theoretic sense. This disproves Kuznetsov's conjecture and the sufficiency of the associated-K3 criterion (and of Fano variety birational to a K3 Hilbert square). The threshold is ineffective; no specific discriminant is shown irrational, the necessity direction is untouched, and stable rationality is not decided. These are not the first irrational cubic fourfolds: the paper cites Katzarkov-Kontsevich-Pantev-Yu (very general cubic) and Fay (some special divisors). parent of this event
Huybrechts, The K3 category of a cubic fourfold: an update (2025), Conjecture 2.1 evidence for this event
Kuznetsov, Derived categories of cubic fourfolds (arXiv 0808.3351), Conjecture 1.1 evidence for this event
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