Primitive Collections and Toric Varieties

Details Primitive Collections and Toric Varieties Primitive Collections and Toric Varieties

2008-08-13

arxiv.org/abs/0808.1836v2

Mathematics

Algebraic Geometry

A new proof of Batyrev's theorem, based on ideas of Kresch, is included and Conjecture 4.4 has been deleted since it is wrong

Scientific paper

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.

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