Equivariant pliability of the projective space

TL;DR

This paper classifies finite subgroups of PGL(4,C) that prevent the projective 3-space from being birationally equivalent to certain fibrations, and describes related G-Mori fibre spaces.

Contribution

It provides a complete classification of specific finite subgroups of PGL(4,C) and details the G-Mori fibre spaces birational to P^3 for these groups.

Findings

Identified all finite subgroups G where P^3 is not G-birational to conic bundles or del Pezzo fibrations.

Explicitly described all G-Mori fibre spaces G-birational to P^3 for these subgroups.

Established criteria for G-birational equivalence in the context of projective 3-space.

Abstract

We classify finite subgroups $G\subset\mathrm{PGL}_4(\mathbb{C})$ such that $\mathbb{P}^3$ is not $G$-birational to conic bundles and del Pezzo fibrations, and explicitly describe all $G$-Mori fibre spaces that are $G$-birational to $\mathbb{P}^3$ for these subgroups.