Modular Lines for Singularities of the T-series
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Unimodular functions have a μ-constant line in their miniversal unfoldings. Their miniversal deformations on the other hand contain a nontrivial τ-constant stratum only for the three cases of elliptic singularities. In computer experiments we found six sub-series of the T-series, which have a modular line in the their miniversal deformations. The singular locus of the family restricted to such a line splits into an elliptic singularity and another one of A k-type, such that the deformation is τ-constant along the modular line. Each modular line can be patched together with the modular line of the associated elliptic singularity, completing it at infinity. All computations are based on the author’s algorithm for computing modular spaces as flatness stratum of the relative cotangent cohomology inside a deformation.
KeywordsUnimodal Singularities Deformations of singularities Modularity
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