Hypertoric variety

In mathematics, a hypertoric variety or toric hyperkähler variety is a quaternionic analog of a toric variety constructed by applying the hyper-Kähler quotient construction of N. J. Hitchin, A. Karlhede, and U. Lindström et al. (1987) to a torus acting on a quaternionic vector space. Roger Bielawski and Andrew S. Dancer (2000) gave a systematic description of hypertoric varieties.

References

• Bielawski, Roger; Dancer, Andrew S. (2000), "The geometry and topology of toric hyperkähler manifolds", Communications in Analysis and Geometry 8 (4): 727–760, doi:10.4310/CAG.2000.v8.n4.a2, http://www1.maths.leeds.ac.uk/~rb/short.pdf 
• Hitchin, N. J.; Karlhede, A.; Lindström, U.; Roček, M. (1987), "Hyper-Kähler metrics and supersymmetry", Communications in Mathematical Physics 108 (4): 535–589, doi:10.1007/BF01214418, http://projecteuclid.org/euclid.cmp/1104116624