Meaning of toric | Babel Free

Definitions

1. Pertaining to or shaped like a torus, or a section of a torus; toroidal.
2. Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
3. Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia
4. (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group.
5. Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus.
6. Generated by differences of monomials.
7. A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia

Equivalents

Examples

“The study of toric varieties is a wonderful part of algebraic geometry. There are elegant theorems and deep connections with polytopes, polyhedra, combinatorics, commutative algebra, symplectic geometry, and topology. Toric varieties also have unexpected applications in areas as diverse as physics, coding theory, algebraic statistics, and geometric modeling. Moreover, as noted by Fulton [105], "toric varieties have provided a remarkably fertile testing ground for general theories.”

CEFR level