Birationally superrigid Fano 3-folds of codimension 4

Abstract

We determine birational superrigidity for a quasismooth prime Fano $3$-fold of codimension $4$ with no projection centers. In particular we prove birational superrigidity for Fano $3$-folds of codimension $4$ with no projection centers which were recently constructed by Coughlan and Ducat. We also pose some questions and a conjecture regarding the classification of birationally superrigid Fano $3$-folds.