The stability threshold and Diophantine approximation

Abstract

The purpose of this paper is to use the filtration that appeared in Ru and Vojta [Amer. J. Math. 142 (2020), pp. 957-991] to extend the result of Blum-Jonsson [Adv. Math. 365 (2020), p. 57], as well as to explore some connections between the notion of the K K -stability and Diophantine approximation, especially the β \beta -constant and the Ru-Vojta’s theorem.