@article{8217badec63144829a57ffb9bda75a85,
title = "A pathology of asymptotic multiplicity in the relative setting",
abstract = "We point out an example of a projective family π: X → S, a sub-variety V ⊂ X, and a π-pseudoeffective divisor D on X for which the asymptotic multiplicity σv(D; X/S) is infinite. This shows that the divisorial Zariski decomposition is not always defined for pseudoeffective divisors in the relative setting.",
author = "John Lesieutre",
note = "Funding Information: I am grateful to the referee for a careful reading and many useful suggestions, as well as to James McKernan for helpful discussions. This material is based upon work supported by the National Science Foundation under agreement No. DMS-1128155. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.",
year = "2016",
doi = "10.4310/MRL.2016.v23.n5.a9",
language = "English (US)",
volume = "23",
pages = "1433--1451",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "5",
}