On K-stability of Fano's last Fanos

TL;DR

This paper investigates the K-stability of specific smooth Fano threefolds of Picard rank 2 and degree 22, obtained via blow-ups, and describes their automorphism groups.

Contribution

It provides the first analysis of K-stability for these particular Fano threefolds and details their automorphism groups.

Findings

Determined K-stability status of the threefolds.

Described automorphism groups explicitly.

Linked geometric construction to stability properties.

Abstract

We study K-stability of smooth Fano threefolds of Picard rank $2$ and degree $22$ which can be obtained by blowing up a smooth complete intersection of two quadrics in $\mathbb{P}^5$ along a conic. We also describe the automorphism groups of these threefolds.