K-Polystable Toric Fano Varieties With Small Alpha Invariants

For every $n\ge2$ the paper exhibits an $n$-dimensional K-polystable toric $\mathbb{Q}$-Fano variety whose alpha invariant is exactly $\tfrac{2}{2n+1}$, answering a question of Liu and Zhuang on whether a K-semistable example exists with alpha invariant between $\tfrac{1}{n+1}$ and $\tfrac1n$.

Result

Proved

Status

Resolved

AI contribution

AI-discovered

Method

Construction

Field

Algebraic Geometry, K-Stability

Posed by

Yuchen Liu and Ziquan Zhuang

Year posed

2022

Years open

4y

Solved

2026-07-04

Model

ChatGPT 5.5 Pro + Danus

Vendor

OpenAI; Frenzy Math

Collaborators

Jihao Liu, Ziwen Zhu

Verification

Unreviewed

Publication

Preprint

Significance

15 / 100*

Disclosed cost

—

Wikipedia

No dedicated article