Remarks on the group of birational selfmaps of a conic fibration

TL;DR

This paper investigates the structure of the group of birational selfmaps of a conic bundle variety, revealing a surjective morphism to an uncountably infinite direct sum of
72/2
72 groups.

Contribution

It establishes a new understanding of the algebraic structure of birational selfmaps for conic fibrations, highlighting their complex infinite subgroup composition.

Findings

The group admits a surjective morphism to an uncountable sum of
72/2
72 groups.

The structure of birational selfmaps is more intricate than previously understood.

Provides insights into the algebraic properties of conic bundle automorphisms.

Abstract

We study the group of birational selfmaps of a variety birational to a conic bundle. We prove that it admits a surjective morphism to the direct sum of an uncountable number of copies of $\mathbb Z/2\IZ$.