具有几何K3范畴的无理三次四维簇
Irrational cubic fourfolds with geometric K3 categories
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具体内容
稿件研究Hassett判别式充分大的三次四维簇的有理性。作者声称对每个充分大的容许Hassett判别式，该判别式的非常一般三次四维簇不可理，尽管其Kuznetsov分量等价于某个射影K3曲面的通常导出范畴；判别式阈值非有效。摘要表示这否定Kuznetsov有理性猜想，并因这些三次簇在Hodge理论意义下对应无扭极化K3曲面，也否定关联K3有理性预测的充分性方向。
- 对充分大容许Hassett判别式的非常一般三次四维簇证明不可理
- 其Kuznetsov分量仍等价于射影K3曲面的导出范畴
- 判别式阈值非有效，并据此否定Kuznetsov有理性猜想
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英文原始摘要
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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