Jacobian Variety

In algebraic geometry, the Jacobian variety of a non-singular algebraic curve of genus g is the moduli space of degree zero line bundles on the curve, equivalently the connected component of the identity in the curve own Picard group, making it an abelian variety. It is named after Carl Gustav Jacobi and is a principally polarized abelian variety of dimension g. Over the complex numbers it is a complex torus, and any algebraic curve can be embedded into its own Jacobian variety.