= Fan in toric geometry
{title2=$\Sigma$}
= Toric fan
{synonym}
A <fan in toric geometry> is a finite collection of rational strongly convex <cones in toric geometry> in a real <vector space> with a <lattice>, closed under taking <faces of a polyhedral cone>, such that the intersection of two cones is a face of each. A fan determines a <toric variety>.
A fan $\Sigma$ in $N_{\mathbb R}$ is a finite collection of strictly convex rational polyhedral cones closed under taking faces, such that the intersection of two cones is a face of each.
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