Finite collineation groups and birational rigidity

TL;DR

This paper classifies finite groups acting on projective 3-space that preserve its birational rigidity, advancing understanding of symmetries in algebraic geometry.

Contribution

It provides a classification of finite groups in PGL(4,C) that ensure the birational rigidity of the projective 3-space.

Findings

Identified all finite groups G in PGL(4,C) with G-birationally rigid action on P^3.

Established criteria for birational rigidity related to group actions.

Contributed to the broader understanding of symmetry and rigidity in algebraic varieties.

Abstract

We classify finite groups $G$ in $\mathrm{PGL}_{4}(\mathbb{C})$ such that $\mathbb{P}^3$ is $G$-birationally rigid.