  In this paper we formulate a conjecture which partially generalizes the
Gross-Kohnen-Zagier theorem to higher weight modular forms. For f in S_k(N)
satisfying certain conditions, we construct a map from the Heegner points of
level N to a complex torus defined by f. We define higher weight analogues of
Heegner divisors on this torus. We conjecture they all lie on a line, and their
positions are given by the coefficients of a certain Jacobi form corresponding
to f. In weight 2, our map is the modular parametrization map (restricted to
Heegner points), and our conjectures are implied by Gross-Kohnen-Zagier. For
any weight, we expect that our map is the Abel-Jacobi map on a certain modular
variety, and so our conjectures are consistent with the conjectures of
Beilinson-Bloch. We have verified our map is the Abel-Jacobi for weight 4. We
provide numerical evidence to support our conjecture for a variety of examples.
