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On a vanishing theorem due to Bogomolov

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arxiv 2011.13751 v1 pith:XOY46ZS2 submitted 2020-11-27 math.CV math.AG

Xiaojun Wu This is my paper · ORCID
classification math.CVmath.AG
keywords bogomolovlinevanishingahlerarbitraryassumptionboucksombundle
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In this note, we give a new proof of a vanishing result originally due to Bogomolov, and later generalised by Mourougane and Boucksom. The statement holds for arbitrary pseudoeffective line bundles over compact K\"ahler manifolds, under an assumption on the numerical dimension of the line bundle.

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  1. A Bogomolov type vanishing theorem

    math.AG 2026-07 conditional novelty 5.0 of 10

    If α is nef and c1(L)−α is a positive current, then H^n(X, Ω_X^p ⊗ L ⊗ I(ψ)) = 0 for p ≥ n − nd(α) + 1.

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