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