Packing Integral Tori in Del Pezzo Surfaces

We extend a packing result of R. Hind and E. Kerman for integral Lagrangian tori in S^2 x S^2 to the Del Pezzo surfaces D_n, omega_Dn for n = 1,...,5. An integral torus is one whose relative area homomorphism is integer-valued, and we seek a maximal integral packing. By definition, this is a disjoint collection {L_i} of integral Lagrangian tori with the following property: any other integral Lagrangian torus not in this collection must intersect at least one of the L_i. We show that one can always find such a packing consisting of only the Clifford torus.