Conn
swMATH ID:  8599 
Software Authors:  Eriksen, E.; Gustavsen, T. S. 
Description:  Conn.lib, A singular library for connections on modules: Computing obstructions for existence of connections on modules. 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 AnAn, DnDn or EnEn, only the free MCM modules admit connections if n≤50n≤50 
Homepage:  http://www.sciencedirect.com/science/article/pii/S0747717106001106 
Related Software:  SINGULAR 
Cited in:  2 Documents 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Computing obstructions for existence of connections on modules. Zbl 1127.13011 Eriksen, Eivind; Gustavsen, Trond Stølen 
2007

Cited by 2 Authors
2  Eriksen, Eivind 
2  Gustavsen, Trond Stølen 
Cited in 2 Serials
1  Journal of Pure and Applied Algebra 
1  Journal of Symbolic Computation 
Cited in 4 Fields
2  Commutative algebra (13XX) 
2  Algebraic geometry (14XX) 
1  Several complex variables and analytic spaces (32XX) 
1  Computer science (68XX) 