Nonrational del Pezzo fibrations admitting an action of the Klein simple group

TL;DR

This paper constructs specific degree 2 del Pezzo fibrations with Klein simple group actions and proves their nonrationality using Kollár's reduction modulo p method, contributing to understanding Klein group embeddings in Cremona groups.

Contribution

It introduces new examples of del Pezzo fibrations with Klein simple group symmetry and establishes their nonrationality, advancing the study of group actions in algebraic geometry.

Findings

Constructed del Pezzo fibrations with Klein simple group action

Proved nonrationality using reduction modulo p method

Linked group embeddings to birational geometry properties

Abstract

We present a series of del Pezzo fibrations of degree $2$ admitting an action of the Klein simple group and prove their nonrationality by the reduction modulo $p$ method of Koll\'{a}r. This is relevant to embeddings of the Klein simple group into the Cremona group of rank $3$.