A survey of hypertoric geometry and topology

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.

References in corpus (6)

• Toric Hyperkahler Varieties
• Absolutely indecomposable representations and Kac-Moody Lie algebras (with an appendix by Hiraku Nakajima)
• Hyperkahler analogues of Kahler quotients
• The Orbifold Chow Ring of Hypertoric Deligne-Mumford Stacks
• A nonhausdorff model for the complement of a complexified arrangement
• Complete hyperkaehler 4n-manifolds with a local tri-Hamiltonian R^n-action

Cited by in corpus (13)

• Boundaries, Mirror Symmetry, and Symplectic Duality in 3d $\mathcal{N}=4$ Gauge Theory
• Quantizations of conical symplectic resolutions I: local and global structure
• Localization algebras and deformations of Koszul algebras
• On Deformation Quantizations of Hypertoric varieties
• Faithful tropicalization of hypertoric varieties
• Strong regular embeddings of Deligne-Mumford stacks and hypertoric geometry
• Elliptic canonical bases for toric hyper-Kahler manifolds
• An algebro-geometric realization of the cohomology ring of Hilbert scheme of points in the affine plane
• Ehrhart Theory for Lawrence Polytopes and Orbifold Cohomology of Hypertoric Varieties
• The Orlik-Terao algebra and the cohomology of configuration space
• Fibred toric varieties in toric hyperkähler varieties
• Holomorphic Lagrangian fibrations of toric hyperkahler manifolds
• Cotangent bundles of toric varieties and coverings of toric hyperkähler manifolds