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arXiv · 2607.04005

K-polystable toric Fano varieties with small alpha invariants

Jihao Liu·Ziwen Zhu
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Abstract

For every $n\geq 2$, we exhibit an $n$-dimensional K-polystable toric $\mathbb{Q}$-Fano variety $X_n$, defined by the face fan of an explicit lattice polytope, and whose alpha invariant is exactly $\tfrac{2}{2n+1}$. This answers a question of Liu and Zhuang whether there exists an $n$-dimensional K-semistable $\mathbb{Q}$-Fano variety whose alpha invariant is between $\tfrac{1}{n+1}$ and $\tfrac1n$. The main result of this paper was obtained by Chatgpt 5.5 pro, and the Danus system based on the Rethlas system.

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Jihao Liu, Ziwen Zhu. 2026-07-04. K-polystable toric Fano varieties with small alpha invariants. https://arxiv.org/abs/2607.04005

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