algebraic geometry
Noun
Meaning
algebraic geometry (countable and uncountable, plural algebraic geometries)
(mathematics) A branch of mathematics that studies algebraic varieties (solution sets of polynomial equations) and their generalisations, using techniques from both algebra (chiefly commutative algebra) and geometry.
Synonyms
Related terms
Examples
Another formal generalization is possible to Universal algebraic geometry in which every variety of algebras has its own algebraic geometry.
Atiyah and Ward used the Penrose correspondence to reduce the classification of all instantons on the 4-sphere to a problem in algebraic geometry.
A notable exception to modern algebraic geometry texts following the conventions of this article is Commutative algebra with a view toward algebraic geometry / David Eisenbud (1995), which uses "h A " to mean the covariant hom-functor.
Grothendieck laid a new foundation for algebraic geometry by making intrinsic spaces ("spectra") and associated rings the primary objects of study.
For these reasons, projective space plays a fundamental role in algebraic geometry.
History Prehistory: before the 16th century Some of the roots of algebraic geometry date back to the work of the Hellenistic Greeks from the 5th century BC.