Albanese map for Kähler manifolds with nef anticanonical bundle

Titelangaben

Naumann, Philipp ; Wu, Xiaojun:
Albanese map for Kähler manifolds with nef anticanonical bundle.
In: Mathematische Zeitschrift. Bd. 311 (2025) . - 25.
ISSN 1432-1823
DOI der Verlagsversion: https://doi.org/10.1007/s00209-025-03810-x

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Abstract

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.