Scaling Behavior on the Space of Calabi-Yau Manifolds

Recent work is reviewed which suggests that certain universal quantities, defined for all Calabi-Yau manifolds, exhibit a specific behavior which is not present for general K\"ahler manifolds. The variables in question, natural from a mathematical perspective, are of physical importance because they determine aspects of the low-energy string physics in four dimensions, such as Yukawa couplings and threshold corrections. It is shown that these quantities, evaluated on the complete class of Calabi-Yau hypersurfaces in weighted projective 4-space, exhibit scaling behavior with respect to a new scaling variable. (To appear in Mirror Symmetry II.)