The transitions between neighbouring plateaux in the quantum Hall system are observed to follow anti-holomophic scaling with superuniversal scaling exponents, showing that the system contains an emergent sub-modular discrete symmetry and a holomorphic structure at low energies. We identify a class of effective scaling models consistent with this data, which is parametrized by the complex structure of a torus with a special spin structure, in which only the number of fermions (c) remains

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... ined. For c = 2 this gives the superuniversal anti-holomorphic scaling potential previously inferred from data, with scaling exponent nu = 2.6, in reasonable agreement with available scaling data.