RESOLVING SINGULARITIES IN (0,2) MODELS

In contrast to the familiar (2, 2) case, the singularities which arise in the (0, 2) setting can be associated with degeneration of the base Calabi-Yau manifold and/or with degenerations of the gauge bundle. We study a variety of such singularities and give a procedure for resolv ing those which can be cured perturbatively. Among the novel features which emerge are models in which smoothing singularities in the base y ields a gauge sheaf as opposed to a gauge bundle as the structure to w hich left-moving fermions couple. Supersymmetric a-models with target data being an appropriate sheaf on a Calabi-Yau space therefore appear to be the natural arena for N = 1 string models in four dimensions. W e also indicate a variety of singularities which would require a non-p erturbative treatment for their resolution and briefly discuss applica tions to heterotic models on K3.