The Method of Computing Formal Moduli

✍ Scribed by Arvid Siqveland

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 228 KB
• Volume: 241
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.2001.8757

✦ Synopsis

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 E . Finally we discuss the degeneracy properties of these mod-6 ules, 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 Ž 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 .