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<p>We study the structure of the Albanese map for Kähler manifolds with nef anticanonical bundle. First, we give a result for fourfolds whose Albanese torus is an elliptic curve. In the general case, for manifolds of arbitrary dimension, we consider two cases: the general fiber of the Albanese map is either a Calabi-Yau manifold or a projective space. In the first case, we show that the manifold itself must be Calabi-Yau. In the second case, we provide a more topological proof of a result by Cao and Höring, which states that the manifold must be the projectivization of a numerically flat vector bundle.</p>

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Albanese map for Kähler manifolds with nef anticanonical bundle

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  • 发表日期：

    2025年7月25日

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  • Philipp Naumann,
  • Xiaojun Wu

摘要

We study the structure of the Albanese map for Kähler manifolds with nef anticanonical bundle. First, we give a result for fourfolds whose Albanese torus is an elliptic curve. In the general case, for manifolds of arbitrary dimension, we consider two cases: the general fiber of the Albanese map is either a Calabi-Yau manifold or a projective space. In the first case, we show that the manifold itself must be Calabi-Yau. In the second case, we provide a more topological proof of a result by Cao and Höring, which states that the manifold must be the projectivization of a numerically flat vector bundle.