MODULAR-FORMS AND INSTANTON NUMBERS IN N=2 DUAL STRING PAIRS

In this lecture we review some contributions to the study of dynamical questions in N = 2 supersymmetric string compactifications. The recur rent themes are the relation between perturbative heterotic couplings, expressed in terms of certain modular forms, and the corresponding ty pe II couplings, determined by genus g instanton numbers. The investig ation is performed concentrating on the N = 2 prepotential and on the gravitational coupling F-1, for a particular heterotic/type II dual st ring pair. The relation to the N = 4 situation is also briefly discuss ed.