Orbifold cohomology of hypertoric varieties

Details Orbifold cohomology of hypertoric varieties Orbifold cohomology of hypertoric varieties

2006-07-18

arxiv.org/abs/math/0607421v2

Internat. J. Math. 19 (2008), no. 8, 927--956.

Mathematics

Differential Geometry

27 pages, 2 figures

Scientific paper

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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