A pathology of asymptotic multiplicity in the relative setting

We point out an example of a projective family $π: X \to S$, a $π$-pseudoeffective divisor $D$ on $X$, and a subvariety $V \subset X$ for which the asymptotic multiplicity $σ_V(D;X/S)$ is infinite. This shows that the divisorial Zariski decomposition is not always defined for pseudoeffective divisors in the relative setting.

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