A pathology of asymptotic multiplicity in the relative setting

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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.

Original languageEnglish (US)
Pages (from-to)1433-1451
Number of pages19
JournalMathematical Research Letters
Volume23
Issue number5
DOIs
StatePublished - 2016

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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