mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

, a hypertoric variety or toric hyperkähler variety is a

quaternion In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. Hamilton defined a quatern ...

ic analog of a

toric variety In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Some authors also require it to be nor ...

constructed by applying the hyper-Kähler quotient construction of to a torus acting on a

quaternionic vector space In mathematics, a left (or right) quaternionic vector space is a left (or right) H-module (mathematics), module where H is the (non-commutative) division ring of quaternions. The space H''n'' of ''n''-tuples of quaternions is both a left and right ...

. gave a systematic description of hypertoric varieties.

References

* *{{citation, mr=0877637 , last1=Hitchin, first1= N. J., last2= Karlhede, first2= A., last3= Lindström, first3= U., last4= Roček, first4= M. , title=Hyper-Kähler metrics and supersymmetry , journal=Communications in Mathematical Physics, volume= 108 , year=1987, issue= 4, pages= 535–589, doi=10.1007/BF01214418, s2cid=120041594 , url=http://projecteuclid.org/euclid.cmp/1104116624 Algebraic geometry