PreprintarXiv licencearXiv
K-stability of a class of smooth Fano complete intersections
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.
Related
- K-stability and birational rigidity of Fano 3-fold weighted complete intersections
- Wall-crossing formula and genus-one Virasoro conjecture for Fano complete intersections
- Hodge level and effective non-vanishing for smooth weighted complete intersections
- Slope stability of tangent bundles of smooth toric Fano varieties
- Motivic classes of Fano schemes of lines on intersections of two quadrics
BibTeX
@misc{hu2026kstability,
title = {{K-stability of a class of smooth Fano complete intersections}},
author = {Yijue Hu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03311},
eprint = {2610.03311},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03311},
}
RIS
TY - UNPB
TI - K-stability of a class of smooth Fano complete intersections
AU - Yijue Hu
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03311
UR - https://arxiv.org/abs/2610.03311
AB - 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.
ER -