无需量子计算的无理性原子判据
An atomic criterion for irrationality without quantum computations
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中文总结 AI 辅助
该研究提出一种无需量子计算、基于原子理论的无理性判据，结合量子乘法单值群等变性与单值群表示不可约性，可判定三类特殊代数簇的无理性。
中文摘要 AI 辅助
Katzarkov-Kontsevich-Pantev-Yu引入的双有理不变量可用于获得量子上同态性质良好的代数簇的无理性结果。我们发现，在特定上同调条件下，无需实际计算原子，仅利用量子乘法的单值群等变性和单值群表示的不可约性，就能从原子理论中推导出非常一般的代数簇的无理性。该判据适用于已被证实无理性的非常一般的三次四维簇和Gushel-Mukai四维簇，还适用于指数为1的Fano流形中非常一般的(c5)型Kuchle四维簇。
英文摘要
The birational invariants introduced by Katzarkov-Kontsevich-Pantev-Yu allows one to obtain irrationality results for varieties whose quantum cohomology is well-behaved. We observe that under certain cohomological conditions, we can deduce irrationality of a very general member from the theory of atoms without actually computing them, using only monodromy equivariance of quantum multiplication and irreducibility of the monodromy representation. Our criterion applies to the very general cubic and Gushel-Mukai fourfolds, whose irrationalities were already known, but also to the very general K{ü}chle fourfold of type (c5), which is a Fano manifold of index one.
