I know the question is not very rigorous, but I have been trying to prove some facts about toric varieties and I think giving this set some structure would be very helpful.

So, suppose you fix a lattice $N$. What do we know about the set of fans in this lattice?

  • $\begingroup$ I don't know anything about toric varieties and fans, but you got me looking them up on Wikipedia, and I saw something that looked wrong: "The toric variety of a fan is given by taking the affine toric varieties of its cones and gluing them together by identifying $U_\sigma$ with an open subvariety of $U_\tau$ whenever $\sigma$ is a face of $\tau$. Conversely, every fan of strongly convex rational cones has an associated toric variety." Did that literally just say "We can do a thing. Conversely, we can do that same thing."? $\endgroup$ Dec 3, 2016 at 15:03
  • $\begingroup$ @Dustan Yes, it did. $\endgroup$
    – svelaz
    Dec 3, 2016 at 15:13
  • $\begingroup$ Alright, I'm not crazy. Hopefully somebody who actually knows something will come along and see my comment and correct it on Wikipedia. $\endgroup$ Dec 3, 2016 at 15:15


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