Convexity and Zariski decomposition structure

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...

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Published inGeometric and functional analysis Vol. 26; no. 4; pp. 1135 - 1189
Main Authors Lehmann, Brian, Xiao, Jian
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.07.2016
Springer Nature B.V
Springer Verlag
Subjects
Analysis
Convexity
Decomposition
Mathematics
Mathematics and Statistics
Transformations (mathematics)
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-016-0384-5