α(X,Δ,L) and δ(X,Δ,L) are computed by quasi-monomial valuations for projective klt pairs over algebraically closed fields of char 0, without uncountability assumptions.
Fujino.Foundations of the minimal model program, volume 35 ofMSJ Memoirs
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The normalized local volume of a non-closed point equals an expression built from the normalized local volumes of closed points.
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On the quasi-monomiality of the $\alpha$- and $\delta$-invariants
α(X,Δ,L) and δ(X,Δ,L) are computed by quasi-monomial valuations for projective klt pairs over algebraically closed fields of char 0, without uncountability assumptions.
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On the normalized local volume of a non-closed point
The normalized local volume of a non-closed point equals an expression built from the normalized local volumes of closed points.