Concept information
Preferred term
algebraic variety
Definition
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Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Algebraic_variety)
Broader concept
Narrower concepts
- affine variety
- algebraic curve
- algebraic group
- algebraic surface
- Bombieri-Lang conjecture
- Calabi-Yau manifold
- codimension
- field of definition
- function field of an algebraic variety
- Grassmannian
- Hasse-Weil zeta function
- Hessenberg variety
- hypersurface
- intersection theory
- Krull dimension
- local zeta function
- Manin conjecture
- Mordellic variety
- projective variety
- rational point
- rational variety
- tangent cone
- toric variety
- transcendental extension
In other languages
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French
URI
http://data.loterre.fr/ark:/67375/PSR-ZGXHSTNB-1
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