English

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.

Keywords

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!

R2 v1 2026-07-01T05:46:45.838Z