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Abundance theorem for minimal compact K\"ahler manifolds with vanishing second Chern class

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arxiv 2205.10613 v1 pith:FC7KK3ZH submitted 2022-05-21 math.AG math.CVmath.DG

classification math.AGmath.CVmath.DG
keywords bundleahlercompactcotangentabundancecanonicalchernclass
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abstract

In this paper, for compact K\"ahler manifolds with nef cotangent bundle, we study the abundance conjecture and the associated Iitaka fibrations. We show that, for a minimal compact K\"ahler manifold, the second Chern class vanishes if and only if the cotangent bundle is nef and the canonical bundle has the numerical dimension $0$ or $1$. Additionally, in this case, we prove that the canonical bundle is semi-ample. Furthermore, we give a relation between the variation of the fibers of the Iitaka fibration and a certain semipositivity of the cotangent bundle.

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Cited by 3 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. Compact K\"ahler manifolds with nef anti-canonical bundle

    math.AG 2025-06 conditional novelty 7.0 of 10

    Every compact Kähler manifold with nef anti-canonical bundle admits a locally trivial fibration over a Calabi-Yau manifold with rationally connected fibers.

  3. 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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