2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137613In this survey article we describe the geometry of toric hyperkähler varieties, which are hyperkähler quotients of the quaternionic vector spaces by tori. In particular, we discuss the Betti numbers, the cohomology ring, and variation of hyperkähler structures of these spaces with many improved results and proofs.20pages. To appear in AMS Contemporary Mathematics (Proceedings of the Toric Topology Conference, Osaka, JapanDifferential GeometrySymplectic Geometry53C26; 53D20; 14L24text