Rationally connected threefolds with nef and bad anticanonical divisor

TL;DR

This paper classifies smooth rationally connected threefolds with nef but not semi-ample anticanonical divisors, focusing on cases where the divisor is nef but exhibits 'bad' properties.

Contribution

It provides a classification of rationally connected threefolds with nef, non-semi-ample anticanonical divisors, a case not previously well-understood.

Findings

Classification of such threefolds when -K_X is not semi-ample

Identification of properties distinguishing these threefolds

Extension of known results on nef anticanonical divisors

Abstract

Let $X$ be a smooth projective rationally connected threefold with nef anticanonical divisor. We give a classification for the case when $-K_X$ is not semi-ample.