The Method of Computing Formal Moduli

In this paper we consider a method given earlier for computing the formal moduli of modules. We start with a short resume of the method, then we explain how this method can be implemented using a standard basis computation. We list the formal moduli with versal families for all torsionfree rank 1 modules over the curve singularity E6. Finally we discuss the degeneracy properties of these modules, proving that the normalization deforms to all the other torsionfree rank 1 modules. These examples are computed by implementing the algorithm in the Singular language. The program source is not included in this paper for obvious reasons, but can be found in previous work by the author (1997, Implementing the algorithm for computing formal moduli, Preprint Series, Institute of Mathematics, University of Oslo).