Lagrangian interpretation of Abel-Jacobi mappings associated to Fano threefolds

Using the general framework due to Donagi-Markman \cite{DM} and Markushevich \cite{M} we shall derive an expression for the differential of Abel-Jacobi mappings on Fano threefolds. This formula involves information normal to the Lagrangian submanifolds constructed in \cite{DM} and \cite{M}. It may be applied to give new proofs of a number of classical results about these varieties.