Let $X_\Sigma$ be a smooth toric variety corresponding to a fan $\Sigma$, $V(\sigma)\subseteq X_\Sigma$ the closure of the orbit $O(\sigma)$ corresponding to a cone $\sigma$ of $\Delta$. $V(\sigma)$ has codim(d). Furthermore let $U_\sigma$ be the affine toric variety corresponding to the cone $\sigma$ and $V(\sigma)\subseteq U_\sigma=\text{Spec}(A)\subseteq X(\Delta)$.
Why is $V(\sigma)$ defined by a regular sequence $r_1,...,r_d\in A$?