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