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arXiv · 2509.16458

Asymptotics of stability thresholds

Junyao Peng
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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.

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Junyao Peng. 2025-09-19. Asymptotics of stability thresholds. https://arxiv.org/abs/2509.16458

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