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We suggest that a unified description of the integer and fractional phases of the quantum Hall system may be possible if the scaling diagram of transport coefficients is invariant under linear fractional (modular) transformations.In this model the hierarchy of states, as well as the observed universality of critical exponents, are consequences of a discrete SL (2,Z) symmetry acting on the parameter space of an effective quantum-field theory. Available scaling data on the position of delocalization fixed points in the integer case and the position of mobility fixed points in the fractional case agree with the model within experimental accuracy.

The authors compute explicitly all the Hodge numbers for all Calabi-Yau manifolds realised as complete intersections of hypersurfaces in products of complex projective spaces. This determines the essential part of the matter superfield spectrum for the heterotic superstring compactified on any of these manifolds. They use various techniques presented in the recent literature to obtain 265 distinct Hodge diamonds; they exemplify these techniques, giving all necessary details of their computations.

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