The integral cohomology rings of four-dimensional toric orbifolds

Abstract

Let $X(P,\hat{I}»)$ be a 4-dimensional toric orbifold associated to a polygon $P$ and a characteristic function $\hat{I}»$. Assuming that $X(P,\hat{I}»)$ is locally smooth over a vertex of $P$, we determine the integral cohomology ring $H^{\ast }(X(P,\hat{I}»);\mathbb{Z})$ by constructing an explicit basis and expressing the cup products of the basis elements in terms of $P$ and $\hat{I}»$.

41 pages, 7 figures