Toric irrelevant ideal ($B_{\Sigma }$)

In the Cox ring $S=k[z_{\rho }]$, the irrelevant ideal is generated by ${\prod }_{\rho \notin \sigma (1)}{z}_{\rho }$ as $\sigma$ runs over maximal cones. The Cox construction takes the quotient of $\mathrm{Spec}S\setminus V(B_{\Sigma })$ by the diagonalizable group whose character group is the divisor class group.

// Target: geometry-and-topology.bigb