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Derivative of volumes of big cohomology classes

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arxiv 2307.15909 v1 pith:YFQU2WXV submitted 2023-07-29 math.AG math.CV

Duc-Viet Vu This is my paper · ORCID
classification math.AGmath.CV
keywords classclassesderivativedivisorlocusvolumealongcohomology
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We prove that the partial derivative of the volume function of big classes along any real divisor in a compact Kaehler manifold is equal to the numerical restricted volume of that class to the divisor. A consequence of our main result is that the divisorial components of the non-Kaehler locus of a big class lie in fact in the null locus of that class.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A transcendental non-Archimedean Calabi--Yau Theorem with applications to the cscK problem

    math.AG 2025-09 conditional novelty 8.0 of 10

    Uniform K-stability for models implies existence and uniqueness of a cscK metric in any Kähler class, including transcendental (non-projective) classes.

  2. The Miyaoka-Yau inequality for singular varieties with big canonical or anticanonical divisors

    math.AG 2025-07 conditional novelty 7.0 of 10

    For projective klt varieties with big canonical or anticanonical divisor, the Miyaoka-Yau Chern class inequality holds when intersections are taken with the non-pluripolar product.

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