Cluster type varieties

Abstract

Cluster type varieties are compactifications of algebraic tori on which the volume form has no zeros. These form a natural class of varieties that generalizes both toric varieties and cluster varieties. The aim of this article is to introduce the reader to the concept of cluster type varieties and explain some recent results towards the understanding of these varieties. At the same time, we will pose some problems for further research.

31 pages. This is a paper written for the Bootcamp Proceedings of the Summer Research Institute in Algebraic Geometry held at Colorado State University in 2025