Threefolds with nef anticanonical bundles

TL;DR

This paper studies the geometric properties of smooth projective threefolds with nef anticanonical bundles, proving the surjectivity of their Albanese maps and analyzing morphisms to lower-dimensional varieties.

Contribution

It establishes the surjectivity of the Albanese map for threefolds with nef anticanonical bundles and explores related morphisms to curves and surfaces.

Findings

Albanese map of such threefolds is a surjective submersion

Characterization of morphisms to curves and surfaces with nef relative anticanonical bundles

Insights into the structure of threefolds with nef anticanonical bundles

Abstract

We prove that the Albanese map of a smooth projective threefold, whose anticanonical bundle is nef, is a surjective submersion. We also investigate morphisms of threefolds to curves and surfaces whose relative anticanonical bundle are nef.