Double quadrics with large automorphism groups

TL;DR

This paper classifies certain three-dimensional Fano varieties that are double covers of quadrics with specific symmetry groups and examines their rationality properties.

Contribution

It provides a classification of three-dimensional nodal Fano varieties with large automorphism groups as double covers of quadrics and analyzes their rationality.

Findings

Classification of these Fano varieties achieved

Identified conditions for rationality of the varieties

Connected automorphism groups with geometric properties

Abstract

We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality.