 The name derives from the theorem of Abel and Jacobi that two effective divisors are linearly equivalent if and only if they are indistinguishable under the Abel–Jacobi map.In complex algebraic geometry, the Jacobian of a curve "C" is constructed using path integration.Namely, suppose "C" has genus "g", which means topologically that

Geometrically, this homology group consists of (homology classes of) "cycles" in "C", or in other words, closed loops.