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Convexity and Zariski decomposition structure

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Boston College, Chestnut Hill, MA, 02467, USA

    Brian Lehmann

  2. Institut Fourier, Université Grenoble Alpes, 38610, Gières, France

    Jian Xiao

  3. Institute of Mathematics, Fudan University, Shanghai, 200433, China

    Jian Xiao

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  1. Brian Lehmann
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  2. Jian Xiao
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Correspondence to Brian Lehmann.

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Lehmann, B., Xiao, J. Convexity and Zariski decomposition structure. Geom. Funct. Anal. 26, 1135–1189 (2016). https://doi.org/10.1007/s00039-016-0384-5

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