Asymptotics of stability thresholds
Algebraic Geometry
2025-09-23 v1 Differential Geometry
Abstract
We study asymptotic behavior of the stability thresholds of a big line bundle, and prove explicit bounds on the error terms. This answers Jin--Rubinstein--Tian's questions affirmatively. A key step in our proof is to show that the stability thresholds of a big line bundle can always be computed by quasi-monomial valuations. This generalizes Blum--Jonsson's result on the stability thresholds of an ample line bundle.
Cite
@article{arxiv.2509.16458,
title = {Asymptotics of stability thresholds},
author = {Junyao Peng},
journal= {arXiv preprint arXiv:2509.16458},
year = {2025}
}
Comments
56 pages in total (with 17 pages of appendix). Comments are welcome!