Toric Variety

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} then forms a set of rays of a unique complete fan in M, and therefore determines a two-dimensional toric variety X_Gamma.

See also

Algebraic Variety

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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.

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Toric Variety

Cite this as:

Weisstein, Eric W. "Toric Variety." From MathWorld--A Wolfram Web Resource.

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