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

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abstract

In this paper, we show that for any projective klt pair $(X,\Delta)$ and ample line bundle $L$, there exist quasi-monomial valuations computing $\alpha(X,\Delta,L)$ and $\delta(X,\Delta,L)$, independently of whether the base field is countable. This also yields an alternative proof of the existence of valuations computing $\alpha(X,\Delta,L)$ and $\delta(X,\Delta,L)$ that was originally proved by Blum-Jonsson over an uncountable field.

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math.AG 1

years

2026 1

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UNVERDICTED 1

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  • On the normalized local volume of a non-closed point math.AG · 2026-04-30 · unverdicted · none · ref 12 · 2 links · internal anchor

    The normalized local volume of a non-closed point equals an expression built from the normalized local volumes of closed points.