%0 Journal Article %T Notes on Heterotic Compactifications %A E. Sharpe %J Physics %D 1997 %I arXiv %R 10.1016/S0370-2693(98)00684-4 %X In this technical note we describe a pair of results on heterotic compactifications. First, we give an example demonstrating that the usual statement of the anomaly-freedom constraint for perturbative heterotic compactifications (meaning, matching second Chern characters) is incorrect for compactifications involving torsion-free sheaves. Secondly, we correct errors in the literature regarding the counting of massless particles in heterotic compactifications. %U http://arxiv.org/abs/hep-th/9710031v2