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TitleComputing obstructions for existence of connections on modules
Author(s) Eivind Eriksen, Trond Stølen Gustavsen
TypeArticle in Journal
AbstractWe 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 .
KeywordsConnections, Isolated singularities, Maximal Cohen–Macaulay modules, Lie–Rinehart algebras
URL http://www.sciencedirect.com/science/article/pii/S0747717106001106
JournalJournal of Symbolic Computation
Pages313 - 323
Translation No
Refereed No