TITLE: nef Cone of a Toric Variety
QUESTION [7 upvotes]: Is there a systematic/standard way of extracting the nef cone of a toric variety $X$ from its fan (or polytope)? Can I tell from the basis of $A^1(X)$ induced by the one-skeleton, based on coefficients, when a given divisor class is nef?
In particular I am working working with blowups of $\mathbb{P}^n$. I am uncertain if that extra piece of information helps.
I imagine that the answer to my question is yes, but I havent yet found a place where this is cleanly articulated. 
Thanks in advance.

REPLY [7 votes]: What you are interested in is toric Mori theory. This was first written down by Miles Reid back in the 80s (Decomposition of toric morphisms, incidentally to the best of my knowledge the first paper which wrote out the main steps of Mori's programme.) If you google "toric Mori theory", there are plenty of other hits; I checked Wisniewski's nice Toric Mori theory and Fano manifolds which may well do for you.