SMALL VOLUMES IN COMPACTIFIED STRING THEORY

We discuss some of the classical and quantum geometry associated to th e degeneration of cycles within a Calabi-Yau compactification. In part icular, we focus on the definition and properties of quantum volume, e specially as it applies to identifying the physics associated to loci in moduli space where non-perturbative effects become manifest. We dis cuss some unusual features of quantum volume relative to its classical counterpart. (C) 1997 Elsevier Science B.V.