Details:
Title  Computing obstructions for existence of connections on modules  Author(s)  Eivind Eriksen, Trond Stølen Gustavsen  Type  Article in Journal  Abstract  We consider the notion of a connection on a module over a commutative ring, and recall the obstruction calculus for such connections. This obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Gröbner bases, we need the conversion to a description using free resolutions. We describe our implementation in Singular 3.0, available as the library conn.lib. Finally, we use the library to verify some known results and to obtain a new theorem for maximal Cohen–Macaulay (MCM) modules on isolated singularities. For a simple hypersurface singularity of dimension one or two, it is known that all MCM modules admit connections. We prove that for a simple threefold hypersurface singularity of type A n , D n or E n , only the free MCM modules admit connections if n ≤ 50 .  Keywords  Connections, Isolated singularities, Maximal Cohen–Macaulay modules, Lie–Rinehart algebras  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717106001106 
Language  English  Journal  Journal of Symbolic Computation  Volume  42  Number  3  Pages  313  323  Year  2007  Edition  0  Translation 
No  Refereed 
No 
