K\"{a}hler-Einstein metrics on Pasquier's two-orbits varieties

TL;DR

This paper proves the existence of Kähler-Einstein metrics on two special Pasquier two-orbits varieties and presents a new example of a K-unstable Fano manifold with Picard number one.

Contribution

It establishes the existence of Kähler-Einstein metrics on specific Pasquier varieties and introduces a novel K-unstable Fano manifold example.

Findings

Existence of Kähler-Einstein metrics on two Pasquier varieties

Identification of a new K-unstable Fano manifold with Picard number one

Contribution to the classification of Fano manifolds

Abstract

We show that there exist K\"ahler-Einstein metrics on two exceptional Pasquier's two-orbits varieties. As an application, we will provide a new example of K-unstable Fano manifold with Picard number one.