Complement of an affine toric face chart
= Complement of an affine toric face chart
{title2=$U_\sigma\setminus U_\tau=\bigcup_{\gamma\npreceq\tau}V(\gamma)$}
If $\tau\preceq\sigma$, choose $m\in\sigma^\vee\cap M$ with $\tau=\sigma\cap m^\perp$. Then $U_\tau=D(\chi^m)\subset U_\sigma$. Its complement is the union of orbit closures indexed by faces of $\sigma$ that are not faces of $\tau$.
// Target: geometry-and-topology.bigb