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On the Log Abundance for Compact {K{\"a}hler} threefolds II

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arxiv 2306.00671 v4 pith:4TNJXJMD submitted 2023-06-01 math.AG math.CV

classification math.AGmath.CV
keywords deltacompactabundanceahlercanonicalthreefoldarticlearxiv
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abstract

In this article we show that if $(X, \Delta)$ is a log canonical compact K\"ahler threefold pair such that $K_X+\Delta$ is nef and the numerical dimension $\nu(X, K_X+\Delta)=2$, then $K_X+\Delta$ is semi-ample. This result combined with our previous work in arXiv:2201.01202 shows that the log abundance holds for log canonical compact K\"ahler threefold pairs.

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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. 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.

  2. Semipositivity of the orbifold second Chern class in Fujiki's class

    math.AG 2026-07 conditional novelty 6.0 of 10

    For compact normal analytic varieties in Fujiki's class, Miyaoka's inequality holds when the canonical divisor is nef, and the orbifold second Chern class is semipositive when the anti-canonical divisor is nef, under ...

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