toric

English

English Wikipedia has an article on:

toric section

Wikipedia

Etymology

From torus +‎ -ic.

Pronunciation

• (Received Pronunciation) IPA^(key): /ˈtɒɹɪk/, /ˈtɔːɹɪk/
• (General American) IPA^(key): /ˈtɔɹɪk/
• (New York City, Philadelphia) IPA^(key): /ˈtɑɹɪk/
• Rhymes: -ɒɹɪk, -ɔːɹɪk

Adjective

toric (comparative more toric, superlative most toric)

1. Pertaining to or shaped like a torus, or a section of a torus; toroidal.
   1. (geometry, algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.
      • 2024, David A. Cox, John B. Little, Henry K. Schenck, Toric Varieties‎, American Mathematical Society, →ISBN:

        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.

      1. (algebraic geometry, of a variety) 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
      2. (geometry, of a manifold, generalizing the case of toric varieties) (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.
      3. (algebraic geometry, of a stack) 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.
      4. (commutative algebra, of an ideal) Generated by differences of monomials.
   2. (error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia

Derived terms

• toricity

Translations

Translations

Czech: torický French: torique (fr) Italian: torico Polish: armilarny Spanish: tórico (es)

Anagrams

• Citro, Troic