Let , , ..., be distinct primitive elements of a 2-D Lattice such that for , ..., . Each collection then forms a set of rays of a unique complete fan in , and therefore determines a 2-D toric variety .
References
Danilov, V. I. ``The Geometry of Toric Varieties.'' Russ. Math. Surv. 33, 97-154, 1978.
Fulton, W. Introduction to Toric Varieties. Princeton, NJ: Princeton University Press, 1993.
Morelli, R. ``Pick's Theorem and the Todd Class of a Toric Variety.'' Adv. Math. 100, 183-231, 1993.
Oda, T. Convex Bodies and Algebraic Geometry. New York: Springer-Verlag, 1987.
Pommersheim, J. E. ``Toric Varieties, Lattice Points, and Dedekind Sums.'' Math. Ann. 295, 1-24, 1993.