2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129606Hypertoric 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.Algebraic GeometryCombinatorics52C35; 53C26; 14M25; 14F43text