COMMENT ON THE GENERATION NUMBER IN ORBIFOLD COMPACTIFICATIONS

There has been some confusion concerning the number of (1, 1)-forms in orbifold compactifications of the heterotic string in numerous public ations. In this note we point out the relevance of the underlying toru s lattice on this number. We answer the question when different lattic es mimic the same physics and when this is not the case. As a byproduc t we classify all symmetric Z(N)-orbifolds with (2,2) world sheet supe rsymmetry obtaining also some new ones.