AI 中文总结
该研究明确确定n维K-多稳定环面Q-法诺簇的α不变量数值谱，建立完整环面实现定理，强化Liu等的问题并改进其构造结果。
AI 中文摘要
我们明确确定了n维K-多稳定环面Q-法诺簇的普通非等变α不变量的数值谱，具体证明n维K-多稳定环面Q-法诺簇的α(X)集合等于有理数集与区间[1/(n+1),1/2]的交集，该结果建立了完整的环面实现定理，强化了Liu和庄提出的问题，改进了Liu和朱近期的构造结果。
英文摘要
We explicitly determine the numerical spectrum of the ordinary, non-equivariant global invariant for $n$-dimensional K-polystable toric $\mathbb{Q}$-Fano varieties. Specifically, we prove that $$\left\{ α(X)\mid X\text{ is an $n$-dimensional K-polystable toric $\mathbb{Q}$-Fano variety}\right \} = \mathbb{Q}\cap \left[\frac{1}{n+1},\frac{1}{2}\right].$$ This result establishes a complete toric realization theorem, which strengthens a question raised by Liu and Zhuang and refines the recent construction results of Liu and Zhu. The initial construction of the examples in this work was suggested by GPT-5.6 Sol, and was subsequently refined and rigorously developed by the author.
Comments6 pages, no figures. Comments welcome
