K-stability of a class of smooth Fano complete intersections

Yijue Hu

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arXiv · 2610.03311

K-stability of a class of smooth Fano complete intersections

Yijue Hu

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Abstract

We develop an approach to study K-stability of Fano varieties by estimating the local stability threshold along a reducible zero-dimensional subscheme on a smooth curve. As an application, we we show that all smooth index-one Fano hypersurfaces in quadrics are K-stable, when the dimension is higher than one. To prove it, we apply the Abban-Zhuang method to reduce the stability problem to lower dimensions. Specifically, we construct suitable admissible flags such that the last term of the Abban-Zhuang estimate is a local stability threshold along multiple points on a smooth curve, and give a convex geometric interpretation of the estimate.

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Yijue Hu. 2026-10-02. K-stability of a class of smooth Fano complete intersections. https://arxiv.org/abs/2610.03311

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