Abstract
We determine birational superrigidity for a quasi-smooth 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 are recently constructed by Coughlan and Ducat. We also pose some questions and a conjecture regarding the classification of birationally superrigid Fano 3-folds.
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