A generalization to -D of Algebraic Curves. More technically, an algebraic variety is a reduced Scheme of Finite type over a Field . An algebraic variety is defined as the Set of points in the Reals (or the Complex Numbers ) satisfying a system of Polynomial equations for , 2, .... According to the Hilbert Basis Theorem, a Finite number of equations suffices.
See also Abelian Variety, Albanese Variety, Brauer-Severi Variety, Chow Variety, Picard Variety
Ciliberto, C.; Laura, E.; and Somese, A. J. (Eds.). Classification of Algebraic Varieties.
Providence, RI: Amer. Math. Soc., 1994.