PomeDefinition 20.1.32.AB54064E3778 An augmented nef b-divisor over $X$ is a pair $(\mathbb {D},D)$, where
581F18AC54FD$\mathbb {D}$ is a nef b-divisor over $X$;
96DE0B4EFD35$D$ is a formal sum
\[ D=\sum _{E} c_ E E,\quad c_ E\in \mathbb {R}_{\geq 0}, \]where $E$ runs over the set of prime divisors on $X$,
such that the following condition is satisfied:
\[ \sum _{E}c_ E \{ E\} \]
is convergent as a sum in $\mathrm{H}^{1,1}(X,\mathbb {R})$.
The cohomology class of $(\mathbb {D},D)$ is defined as
\[ \mathbb {D}_ X+\sum _{E}c_ E \{ E\} \in \mathrm{H}^{1,1}(X,\mathbb {R}). \]
The volume of $(\mathbb {D},D)$ is defined as
\[ \operatorname{vol}(\mathbb {D},D)=\operatorname{vol}\mathbb {D}. \]
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