We examine the integral cohomology rings of certain families of 2n-dimensional orbifolds X that are equipped with a well-behaved action of the n-dimensional real torus. These orbifolds arise from two distinct but closely related combinatorial sources, namely from characteristic pairs (Q, λ), where Q is a simple convex n-polytope and λ a labelling of its facets, and from ndimensional fans Σ. In the literature, they are referred as toric orbifolds and singular toric varieties respectively. Our first main result provides combinatorial conditions on (Q, λ) or on Σ which ensure that the integral cohomology groups H * (X) of the associated orbifolds are concentrated in even degrees. Our second main result assumes these condition to be true, and expresses the graded ring H * (X) as a quotient of an algebra of polynomials that satisfy an integrality condition arising from the underlying combinatorial data. Also, we compute several examples.

The CW structure of certain spaces, such as effective orbifolds, can be too complicated for computational purposes. In this paper we use the concept of q-CW complex structure on an orbifold, to detect torsion in its integral cohomology. The main result can be applied to well known classes of orbifolds or algebraic varieties having orbifold singularities, such as toric orbifolds, simplicial toric varieties, torus orbifolds and weighted Grassmannians.

No abstract

No abstract

No abstract