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

TL;DR

This paper investigates the second degree cohomology of 4-dimensional toric orbifolds, providing explicit bases and applications to algebraic and divisor group structures.

Contribution

It introduces a new lattice-based method to construct integral cohomology bases and applies it to algebraic and divisor group analysis of toric orbifolds.

Findings

Constructed a basis for degree-two equivariant cohomology using lattice intersections.

Provided an alternative construction for the algebraic cellular basis of integral cohomology.

Determined the Cartier divisor and Picard groups for algebraic toric orbifolds.

Abstract

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.