ABSTRACT

Modular families and modular spaces for quasi-homogeneous isolated complete intersection curve-singularities with modularity one are computed. In particular, it is proved that the modular space of any unimodular singularity has a covering which is biholomorphically equivalent to a punctured or twice punctured Riemann sphere. Some related questions concerning singularities of higher modularity are also discussed.

AMS Classification: Primary 32S15,14H15, 32J05, 14M10, 32G13; Secondary 14H30, 32S05, 32H20, 14D22, 30C45, 30C55