Manifolds with nef anticanonical bundle

Abstract

Let X be a compact Kähler manifold such that the anticanonical bundle $-K_X$ is nef. A classical conjecture claims that the Albanese map 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.

39 pages, changed metadata

References in corpus (2)

• Threefolds with nef anticanonical bundles
• On Fano foliations 2