Chains of N=2, D=4 heterotic type II duals

We report on a search for N = 2 heterotic strings that are dual candidates of type II compactifications on Calabi-Yau threefolds described as K3 fibrations. We find many new heterotic duals by using standard orbifold techniques. The associated type II compactifications fall into chains in which the proposed duals are heterotic compactifications related one another by a sequential Higgs mechanism. This breaking in the heterotic side typically involves the sequence SU(4) --> SU(3) --> SU(2) --> 0, while in the type II side the weights of the complex hypersurfaces and the structure of the K3 quotient singularities also follow specific patterns. Some qualitative features of the relationship between each model and its dual can be understood by fiber-wise application of string-string duality.