Tohoku Mathematical Journal
2009
September
SECOND SERIES VOL. 61, NO. 3

Tohoku Math. J.
61 (2009), 309-332

Title PRIMITIVE COLLECTIONS AND TORIC VARIETIES

Author David A. Cox and Christine von Renesse

(Received August 26, 2008, revised February 19, 2009)
Abstract. 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.

2000 Mathematics Subject Classification. Primary 14M25.
Key words and phrases. Toric varieties, primitive collections.

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