Abelian variety

In algebraic geometry an Abelian variety $A$ over a field $K$ is a projective variety, together with a marked point $0$ and two algebraic maps: addition Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A^2\to A} and inverse Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A\to A} , such that these two maps, and the point $0$ satisfy the Abelian group axioms. One dimensional Abelian varieties are elliptic curves. Over the complex numbers Abelian varieties are as subset of the set of complex tori.