# K\"ahler-Einstein metrics on symmetric general arrangement varieties

## TL;DR

This paper computes Chow quotients of symmetric T-varieties, finds new Kähler-Einstein metrics in complexity two, and characterizes the topology of the orbit space under compact torus actions.

## Contribution

It introduces new examples of Kähler-Einstein metrics on symmetric T-varieties by analyzing their Chow quotients and symmetric alpha invariants.

## Key findings

- New Kähler-Einstein metrics on complexity two T-varieties
- Determination of the homeomorphism class of the orbit space
- Calculation of Chow quotients for specific symmetric T-varieties

## Abstract

We calculate Chow quotients of some families of symmetric \(T\)-varieties. In complexity two we obtain new examples of K\"ahler-Einstein metrics by bounding the symmetric alpha invariant of their orbifold quotients. As an additional application we determine the homeomorpism class of the orbit space of the compact torus action.