  Clemens' conjecture states that the the number of rational curve in a generic
quintic threefold is finite. If it is false we prove that certain periods of
rational curves in such a quintic threefold must vanish. Our method is based on
a generalization of a proof of Max Noether's theorem using infinitesimal
variation of Hodge structures and its reformulation in terms of integrals and
Gauss-Manin connection.
