On the quasi-monomiality of the $\alpha$- and $\delta$-invariants

Abstract

In this paper, we show that for any projective klt pair $(X,\Delta )$ over an algebraically closed field of characteristic \(0\) and any big $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $L$ on $X$, the invariants $\alpha (X,\Delta ,L)$ and $\delta (X,\Delta ,L)$ are computed by quasi-monomial valuations, without any uncountability assumption on the base field.

We have substantially changed the paper. Any comment is welcome