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We clarify the relation between six-dimensional Abelian orbifoldcompactifications of the heterotic string and smooth heterotic K3compactifications with line bundles for both SO(32) and E_8 x E_8 gauge groups.The T^4/Z_N cases for N=2,3,4 are treated exhaustively, and for N=6 someexamples are given. While all T^4/Z_2 and nearly all T^4/Z_3 models have asimple smooth match involving one line bundle only, this is only true for someT^4/Z_4 and T^4/Z_6 cases. We comment on possible matchings with more than oneline bundle for the remaining cases. The matching is provided by comparisons ofthe massless spectra and their anomalies as well as a field theoretic analysisof the blow-ups.Comment: 49 pages, 1 figure; v2: references adde

Merging heterotic orbifolds and K3 compactifications with line bundles