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NormalToricVariety -- the class of all normal toric varieties


A normal toric variety corresponds to a strongly convex rational polyhedral fan. In this package, the fan associated to a normal $d$-dimensional toric variety lies in the rational vector space $\QQ^d$ with underlying lattice $N = \ZZ^d$. The fan is encoded by the minimal nonzero lattice points on its rays and the set of rays defining the maximal cones (a maximal cone is not properly contained in another cone in the fan). More information about the correspondence between normal toric varieties and strongly convex rational polyhedral fans appears in Subsection 3.1 of Cox-Little-Schenck.


To sidestep edge case issues, this package excludes some normal toric varieties. To avoid the $0$-dimensional vector space, all normal toric varieties in this package have positive dimension. Similarly, to circumvent the empty set of rays, all normal toric varieties in this package have an orbit other than the dense algebraic

See also

Functions and methods returning a normal toric variety :

Methods that use a normal toric variety :

For the programmer

The object NormalToricVariety is a type, with ancestor classes Variety < MutableHashTable < HashTable < Thing.