ORBIFOLD COHOMOLOGY OF HYPERTORIC VARIETIES
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Hypertoric varieties are hyperk\"ahler analogues of toric varieties, and are
constructed as abelian hyperk\"ahler quotients of a quaternionic affine space.
Just as symplectic toric orbifolds are determined by labelled polytopes,
orbifold hypertoric varieties are intimately related to the combinatorics of
hyperplane arrangements. By developing hyperk\"ahler analogues of symplectic
techniques developed by Goldin, Holm, and Knutson, we give an explicit
combinatorial description of the Chen-Ruan orbifold cohomology of an orbifold
hypertoric variety in terms of the combinatorial data of a rational cooriented
weighted hyperplane arrangement. We detail several explicit examples, including
some computations of orbifold Betti numbers (and Euler characteristics).
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