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K-Polystable Toric Fano Varieties With Small Alpha Invariants

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k-polystable-toric-fano-small-alphaGeometry & topologyposed by Yuchen Liu and Ziquan Zhuangrecorded: solved

1 attempt · no person has looked

Statement

For every n≥2n\ge2 the paper exhibits an nn-dimensional K-polystable toric Q\mathbb{Q}-Fano variety whose alpha invariant is exactly 22n+1\tfrac{2}{2n+1}, answering a question of Liu and Zhuang on whether a K-semistable example exists with alpha invariant between 1n+1\tfrac{1}{n+1} and 1n\tfrac1n.

Context

Answers a stated question in K-stability by explicit construction, for every dimension at once.

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  • #1

    Attempt 1

    constructionChatGPT 5.5 Pro + Danus with Jihao Liu, Ziwen Zhu ·
    AI involvement
    ai discovered
    — the result was found by a model.
    models
    ChatGPT 5.5 Pro + Danus
    people
    Jihao Liu, Ziwen Zhu

    The abstract states the main result was obtained by ChatGPT 5.5 Pro and the Danus system, an agent built on Rethlas; the proof sketch was likewise produced by the model.

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