Integral bases for the second degree cohomology of 4-dimensional toric orbifolds

We study toric orbifolds of real dimension four with vanishing odd-degree cohomology and obtain a basis for its degree-two equivariant cohomology with integral coefficients by identifying it with the intersection of certain lattices. As applications, we provide an alternative construction of the \emph{algebraic cellular basis} for integral ordinary cohomology \cite{FSS2}. In addition, when the toric orbifold is an algebraic variety, we determine its Cartier divisor group and Picard group.