This paper studies Batyrev's notion of primitive collection. We use primi-tive collections to characterize the nef cone of a quasi-projective tonic variety whose fan hasconvex support, a result stated without proof by Batyrev in the smooth projective case. Whenthe fan is non-simplicial, we modify the definition of primitive collection and explain how ourdefinition relates to primitive collections of simplicial subdivisons. The paper ends with anopen problem.
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