# On iteration of Cox rings

## TL;DR

This paper characterizes varieties with a torus action of complexity one that can undergo multiple Cox ring iterations, advancing understanding of their algebraic structure.

## Contribution

It provides a complete characterization of varieties allowing Cox ring iteration within the specified class, a novel contribution to algebraic geometry.

## Key findings

- Identifies all varieties with complexity one torus action permitting Cox ring iteration
- Establishes criteria for the iteration process to be possible
- Enhances understanding of the structure of Cox rings in algebraic varieties

## Abstract

We characterize all varieties with a torus action of complexity one that admit iteration of Cox rings.