Birational rigidity of del Pezzo fibrations with quotient singularities and its application

TL;DR

This paper establishes a criterion for the birational rigidity of certain del Pezzo fibrations with quotient singularities and demonstrates its application to fibrations with Klein group symmetry.

Contribution

It introduces a new criterion for birational rigidity of del Pezzo fibrations of degrees 1 and 2 with quotient singularities, and applies it to cases with Klein group actions.

Findings

Birational rigidity criterion for degree 1 and 2 del Pezzo fibrations with quotient singularities.

Proved birational rigidity for specific fibrations with Klein simple group symmetry.

Enhanced understanding of birational properties of singular del Pezzo fibrations.

Abstract

In this paper we give a criterion for birational rigidity of del Pezzo fibrations of degree 1 and 2 with only quotient singularities. As an application, we prove birational rigidity of suitable del Pezzo fibrations admitting an action of the Klein simple group.