Primitive Collections and Toric Varieties
Algebraic Geometry
2008-09-03 v2
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 some open problems.
Keywords
Cite
@article{arxiv.0808.1836,
title = {Primitive Collections and Toric Varieties},
author = {David A. Cox and Christine von Renesse},
journal= {arXiv preprint arXiv:0808.1836},
year = {2008}
}
Comments
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