# Birationally superrigid Fano 3-folds of codimension 4

## TL;DR

This paper establishes the birational superrigidity of certain prime Fano 3-folds of codimension 4, expanding the classification of these algebraic varieties and confirming recent constructions.

## Contribution

It proves birational superrigidity for a class of Fano 3-folds of codimension 4 with no projection centers, including recent examples by Coughlan and Ducat.

## Key findings

- Proves birational superrigidity for specific Fano 3-folds
- Confirms recent constructions of Fano 3-folds are superrigid
- Poses questions and conjectures on classification

## 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.