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arXiv · 2310.06695

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

Philipp Naumann·Xiaojun Wu
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Abstract

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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Philipp Naumann, Xiaojun Wu. 2023-10-10. Albanese map for K\"ahler manifolds with nef anticanonical bundle. https://arxiv.org/abs/2310.06695

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