Characterizing volume via cone duality

Jian Xiao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


For divisors over smooth projective varieties, we show that the volume can be characterized by the duality between the pseudo-effective cone of divisors and the movable cone of curves. Inspired by this result, we define and study a natural intersection-theoretic volume functional for 1-cycles over compact Kähler manifolds. In particular, for numerical equivalence classes of curves over projective varieties, it is closely related to the mobility functional studied by Lehmann.

Original languageEnglish (US)
Pages (from-to)1527-1555
Number of pages29
JournalMathematische Annalen
Issue number3-4
StatePublished - Dec 1 2017


  • 32J18
  • 32J25

ASJC Scopus subject areas

  • General Mathematics


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