  I show that anomaly cancellation conditions are sufficient to determine the
two most important topological numbers relevant for Calabi-Yau compactification
to six dimensions. This reflects the fact that K3 is the only non-trivial CY
manifold in two complex dimensions. I explicitly construct the Green-Schwarz
counterterms and derive sum rules for charges of additional enhanced U(1)
factors and compare the results with all possible Abelian orbifold
constructions of K3. This includes asymmetric orbifolds as well, showing that
it is possible to regain a geometrical interpretation for this class of models.
Finally, I discuss some models with a broken $E_7$ gauge group which will be
useful for more phenomenological applications.
