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.Comment: Latex, 21 pages, 2 table