A survey of hypertoric geometry and topology

TL;DR

This survey provides a comprehensive overview of hypertoric geometry and topology, highlighting their connections to matroid combinatorics and their significance in algebraic symplectic and hyperkähler geometry.

Contribution

It consolidates known results and definitions, serving as a reference and introduction to the field of hypertoric varieties and their topological properties.

Findings

Clarifies the relationship between hypertoric varieties and matroids

Summarizes key results in hypertoric geometry and topology

Provides foundational definitions and statements for further research

Abstract

Hypertoric varieties are quaternionic analogues of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry. The aim of this survey is to give clear definitions and statements of known results, serving both as a reference and as a point of entry to this beautiful subject.