A supersymmetric nonlinear σ-model provides us a tool for studying the dynamics of superstrings on a compactified space. If the compactified space is a Ricci-flat Kähler manifold, the nonlinear σ-model has extended superconformal symmetry and the partition function of the model is expressed in terms of characters of the superconformal algebra. The partition function must be modular invariant and this condition gives strong constraints on the spectrum of the model. These constraints are intimately related to geometry of the compactified space. Their implications to particle spectra of the compactified heterotic string theory are also discussed.