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

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“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