  This paper studies Batyrev's notion of primitive collection. We use primitive
collections to characterize the nef cone of a quasi-projective toric variety
whose fan has convex support, a result stated without proof by Batyrev in the
smooth projective case. When the fan is non-simplicial, we modify the
definition of primitive collection and explain how our definition relates to
primitive collections of simplicial subdivisons. The paper ends with some open
problems.
