2009 年 61 巻 3 号 p. 309-332
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 an open problem.
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