Birational rigidity of $G$-del Pezzo threefolds of degree 2

TL;DR

This paper classifies certain degree 2 del Pezzo threefolds with nodes that are $G$-birationally rigid under some subgroup of automorphisms, advancing understanding of their birational properties.

Contribution

It provides a classification of nodal rational non-$Q$-factorial del Pezzo threefolds of degree 2 that exhibit $G$-birational rigidity, a new insight into their structure.

Findings

Identified conditions under which these threefolds are $G$-birationally rigid.

Classified all such threefolds with specific automorphism groups.

Enhanced understanding of birational properties of degree 2 del Pezzo threefolds.

Abstract

In this paper we classify nodal rational non-$\mathbb{Q}$-factorial del Pezzo threefolds of degree 2 which can be $G$-birationally rigid for some subgroup $G\subset \operatorname{Aut}(X)$.