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Convexity and Zariski decomposition structure

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arxiv 1507.04316 v2 pith:FNSGERXC submitted 2015-07-15 math.AG

Brian Lehmann , Jian Xiao This is my paper · ORCID
classification math.AG
keywords decompositionzariskiclassescurvestructuresadmitsauthorconvexity
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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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  1. Slope Stable Sheaves and Hermitian-Einstein Metrics on Normal Varieties with Big Cohomology Classes

    math.AG 2025-01 conditional novelty 6.0 of 10

    Slope stability of reflexive sheaves with respect to big classes is equivalent to existence of T-Hermitian-Einstein metrics when the big class has a birational Zariski decomposition with semiample positive part.

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