Randall F. Westhoff
Computing the Infinitesimal Invariants Associated to Deformations of Subvarieties

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.