Definition:Algebraic Geometry

Definition

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.

Also see

• Definition:Affine Geometry
• Definition:Projective Geometry

• 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.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebraic geometry: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): algebraic geometry