Rationally connected threefolds with nef and bad anticanonical divisor, II

TL;DR

This paper advances the classification of rationally connected threefolds with nef, non-semi-ample anticanonical divisors by analyzing cases where the linear system has a fixed divisor, building on prior work that handled the free case.

Contribution

It extends the classification of such threefolds to include cases with non-zero fixed divisors in the anticanonical linear system.

Findings

Classified new classes of threefolds with fixed divisors in |-K_X|

Identified geometric structures associated with fixed divisors

Extended previous classification results

Abstract

Let $X$ be a smooth complex projective rationally connected threefold with $-K_X$ nef and not semi-ample. In our previous work, we classified all such threefolds when $|{-}K_X|$ has no fixed divisor. In this paper, we continue our classification when $|{-}K_X|$ has a non-zero fixed divisor.