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 1127.13011Eriksen, 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 (13-XX) 2 Algebraic geometry (14-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Computer science (68-XX) Citations by Year