Convexity and Zariski decomposition structure

Brian Lehmann*, Jian Xiao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This is the first part of our work on Zariski decomposition structures, where we study Zariski decompositions using Legendre–Fenchel type transforms. In this way we define a Zariski decomposition for curve classes. This decomposition enables us to develop the theory of the volume function for curves defined by the second named author, yielding some fundamental positivity results for curve classes. For varieties with special structures, the Zariski decomposition for curve classes admits an interesting geometric interpretation.

Original languageEnglish (US)
Pages (from-to)1135-1189
Number of pages55
JournalGeometric and Functional Analysis
Issue number4
StatePublished - Jul 1 2016

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology


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