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Computing the infinitesimal invariants associated to deformations of subvarieties

The purpose of this article is to study and describe a method for computing the innitesimal invariants associated to deformations of subvarieties. An interpretation of the innitesimal invariant of normal functions as a pairing similar to the innitesimal Abel-Jacobi mapping is given. The computation of both invariants for certain forms is then reduced to a residue computation at a nite number of points of the subvariety. Applications of this technique include a nonvanishing result for the innitesimal Abel-Jacobi mapping leading to niteness results for low degree rational curves on complete intersection threefolds with trivial canonical bundle and a generalization of a formula of Voisin for the innitesimal invariant of certain normal functions.