Definition:Algebraic Geometry

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Algebraic geometry is the branch of geometry which studies objects in multi-dimensional space using the techniques of abstract algebra.

In particular, techniques from commutative algebra are mainly used.

It also encompasses the study of algebraic varieties.

Also see

  • Results about algebraic geometry can be found here.

Historical Note

The foundations for the theory of algebraic geometry were laid in Abel's paper Mémoire sur une Propriété Générale d'une Classe Très-Étendue de Fonctions Transcendantes.

It was further developed in the $19$th century by Arthur Cayley.