An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.
Abelian Variety
See also
Albanese Variety, Algebraic Variety, VarietyExplore with Wolfram|Alpha
References
Murty, V. K. Introduction to Abelian Varieties. Providence, RI: Amer. Math. Soc., 1993.Shimura, G. Abelian Varieties With Complex Multiplication and Modular Functions. Princeton, NJ: Princeton University Press, 1999.Shimura, G. and Taniyama, Y. Complex Multiplication of Abelian Varieties and Its Applications to Number Theory. Tokyo: Mathematical Society of Japan, 1961.Referenced on Wolfram|Alpha
Abelian VarietyCite this as:
Weisstein, Eric W. "Abelian Variety." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbelianVariety.html