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Mobile Product and Zariski decomposition

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arxiv 1301.1477 v4 pith:EFDYDLZI submitted 2013-01-08 math.AG math.CV

Mario Principato This is my paper · ORCID
classification math.AGmath.CV
keywords alphaproductlelongmobilenumbersrelationshipclassescohomology
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abstract

We explain the relationship between $\alpha_{1}...\alpha_{q}$ (standard cohomology product) and $(\alpha_{1}...\alpha_{q})$ (mobile intersection product) of pseudo-effective classes $\alpha_{1},...,\alpha_{q}$ on a compact K$\ddot{a}$hler manifold. We also show how to use this relationship for proving some holomorphic Morse inequalities. Then we prove a result concerning the direct image of Lelong numbers under a modification in dimension 3, deriving a continuity property for the Lelong numbers of the wedge of $(1,1)-$currents.

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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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