Abel-Jacobi theorem

The Abel Jacobi theorem is an important result of algebraic geometry. The theory of divisors and the Riemann bilinear relations are fundamental to the developement of this result: if a point O is fixed in a Riemann compact surface X of genus g, the Abel Jaobi map identifies the Picard group: the quotient of divisors of a group of degree zero by the sub-group of divisors associated to meromorphic functions. The Riemann surface of genus g can be embedded in the Jacobian variety via the Abel-Jacobi. In fact, generally.the surface may be provided with an analytical structure.or algebraic varietie.