{"id":"openai-math/Irrational-cubic-fourfolds-with-geometric-K3-categories","pdf":"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","url":"https://github.com/openai/math/tree/main/preprints/Irrational-cubic-fourfolds-with-geometric-K3-categories-September-24-2026","tags":["algebraic-geometry","derived-categories","cubic-fourfolds"],"score":0,"title":"Irrational cubic fourfolds with geometric K3 categories","domain":"Algebraic and complex geometry","family":"054","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.AG","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":3,"published":"2026-09-24","reactions":{},"discussion":[{"url":"https://x.com/ivanswzhang/status/2109305117942186132","date":"2026-10-11","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"},{"url":"https://x.com/ivanswzhang/status/2109582061724119343","date":"2026-10-12","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"},{"url":"https://x.com/ivanswzhang/status/2110157177126260925","date":"2026-10-13","kind":"x","added":"2026-10-24","author":"Shaowu Zhang","handle":"ivanswzhang"}],"formalized":false,"family_title":"Irrational cubic fourfolds with Hodge-theoretic and categorical K3 associations"}