Albanese maps of projective manifolds with nef anticanonical bundles

TL;DR

This paper proves that for projective manifolds with nef anticanonical bundles, the Albanese map is locally isotrivial and a submersion, revealing structural properties of such manifolds.

Contribution

It establishes the local isotriviality and submersion property of the Albanese map for manifolds with nef anticanonical bundles, a new insight into their geometry.

Findings

Albanese map is locally isotrivial.

Albanese map is a submersion.

Structural implications for manifolds with nef anticanonical bundles.

Abstract

Let $X$ be a projective manifold such that the anticanonical bundle $-K_X$ is nef. We prove that the Albanese map $p: X \rightarrow Y$ is locally isotrivial. In particular, $p$ is a submersion.