= Monomial zero locus in an affine toric variety
{title2=$V(\chi^\mu)=\bigcup_{\langle\mu,\tau\rangle\ne0}V(\tau)$}
On the orbit of a face $\tau\preceq\sigma$, the monomial $\chi^\mu$, with $\mu\in\sigma^\vee\cap M$, vanishes exactly when $\mu\notin\tau^\perp$. Its reduced zero locus is consequently the union of those orbit closures. The principal subscheme need not be reduced: $V(x^2)$ and $V(x)$ have the same support but different ideals.
// Target: geometry-and-topology.bigb
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