N=2 SUPERGRAVITY, TYPE-IIB SUPERSTRINGS, AND ALGEBRAIC-GEOMETRY

The geometry of N=2 supergravity is related to the variations of Hodge structure for "formal" Calabi-Yau spaces. All known results in this branch of algebraic geometry are easily recovered from supersymmetry arguments. This identification has a physical meaning for a type IIB superstring compactified on a Calabi-Yau 3-fold. We give exact (non-perturbative) results for the string effective lagrangian. Our geometrical framework suggests a re-formulation of the Gepner conjecture about (2,2) superconformal theories as the solution to the Schottky problem for algebraic complex manifolds having trivial canonical bundle. © 1990 Springer-Verlag.