Toric Variety

Let $m_1$, $m_2$, ..., $m_n$ be distinct primitive elements of a 2-D Lattice $M$ such that ${\rm det}(m_i,m_{i+1})>0$ for $i=1$, ..., $n-1$. Each collection $\Gamma=\{m_1, m_2, \ldots, m_n\}$ then forms a set of rays of a unique complete fan in $M$, and therefore determines a 2-D toric variety $X_\Gamma$.

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.