Threefolds with big and nef anticanonical bundles II

TL;DR

This paper classifies certain smooth complex threefolds with big and nef anticanonical bundles, focusing on cases with Picard number 2 and specific properties of their anticanonical maps and contractions.

Contribution

It extends previous work by classifying threefolds with big and nef anticanonical bundles under new conditions on their contractions and anticanonical maps.

Findings

Classification of threefolds with specified properties

Identification of cases where the anticanonical map is small

Analysis of Mori contractions and flops in these threefolds

Abstract

In continuation of our paper in Math. Ann. 333 we classify smooth complex projective threefolds X with -K_X big and nef but not ample and Picard number 2, whose anticanonical map is small. We assume also that the Mori contraction of X and of its flop are not both birational.