# Birationally rigid complete intersections with a singular point of high multiplicity

## TL;DR

This paper establishes the birational rigidity of certain Fano complete intersections with high-multiplicity singular points, showing they are non-rational and have equal automorphism groups, using advanced singularity and divisor techniques.

## Contribution

It proves birational rigidity for Fano complete intersections with high multiplicity singular points, extending the understanding of their automorphism groups and non-rationality.

## Key findings

- Varieties are non-rational
- Automorphism groups are equal to automorphism groups of biregular automorphisms
- Birational rigidity is established for these varieties

## Abstract

We prove the birational rigidity of Fano complete intersections of index 1 with a singular point of high multiplicity, which can be close to the degree of the variety. In particular, the groups of birational and biregular automorphisms of these varieties are equal, and they are non-rational. The proof is based on the techniques of the method of maximal singularities, the generalized $4n^2$-inequality for complete intersection singularities and the technique of hypertangent divisors.