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arXiv · 2205.10613

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

Masataka Iwai·Shin-ichi Matsumura
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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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Masataka Iwai, Shin-ichi Matsumura. 2022-05-21. Abundance theorem for minimal compact K\"ahler manifolds with vanishing second Chern class. https://arxiv.org/abs/2205.10613

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