On birational involutions of $P^3$

TL;DR

This paper classifies certain involutions on rationally connected threefolds with fixed points, using the equivariant minimal model program to understand their structure and properties.

Contribution

It provides a rough classification of involutions with fixed divisorial components on rationally connected threefolds, advancing understanding of their birational symmetries.

Findings

Classification of involutions with fixed divisorial components

Use of equivariant minimal model program in classification

Insights into the structure of birational involutions

Abstract

Let $X$ be a rationally connected three-dimensional algebraic variety and let $\tau$ be an element of order two in the group of its birational selfmaps. Suppose that there exists a non-uniruled divisorial component of the $\tau$-fixed point locus. Using the equivariant minimal model program we give a rough classification of such elements.