Mathematical Research Letters
Volume 23 (2016)
A pathology of asymptotic multiplicity in the relative setting
Pages: 1433 – 1451
We point out an example of a projective family $\pi : X \to S$, a subvariety $V \subset X$, and a $\pi$-pseudoeffective divisor $D$ on $X$ for which the asymptotic multiplicity $\sigma_V (D; X/S)$ is infinite. This shows that the divisorial Zariski decomposition is not always defined for pseudoeffective divisors in the relative setting.