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Albanese map for K\"ahler manifolds with nef anticanonical bundle

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arxiv 2310.06695 v2 pith:HDIHGCO6 submitted 2023-10-10 math.AG math.CVmath.DG

Philipp Naumann , Xiaojun Wu This is my paper · ORCID
classification math.AGmath.CVmath.DG
keywords albanesebundlecasemanifoldahleranticanonicalcalabi-yaufirst
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We study the structure of the Albanese map for K\"ahler manifolds with nef anticanonical bundle. First, we give a result for fourfolds whose Albanse torus is an elliptic curve. In the general case of any dimension, we look at two cases: The general fiber of the Albanese map is 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 give a more topological proof of a result by Cao and H\"oring which says that the manifold must be a projectivization of a numerically flat vector bundle.

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  1. 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.

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