Manifolds with nef anticanonical bundle
- Resource Type
- research-article
- Authors
- Cao, Junyan; Höring, Andreas
- Source
- Journal für die reine und angewandte Mathematik (Crelles Journal). 2017(724):203-244
- Subject
- Language
- English
- ISSN
- 1435-5345
0075-4102
Let X be a compact Kähler manifold such that the anticanonical bundle -KX$-K_{X}$ is nef. A classical conjecture claims that the Albanese map X→T$X\to T$ is submersive. We prove this conjecture if the general fibre is a weak Fano manifold. If X is projective we prove the conjecture also for fibres of dimension at most two.