Mathematics – Algebraic Geometry
Scientific paper
2006-02-27
J. Symb. Comput. 42 (2007), no. 3, pp. 313-323
Mathematics
Algebraic Geometry
14 pages, LaTeX, paper re-organized, new references added. To appear in Journal of Symbolic Computation
Scientific paper
10.1016/j.jsc.2006.10.001
We consider the notion of a connection on a module over a commutative ring, and recall the obstruction calculus for such connections. The obstruction calculus is defined using Hochschild cohomology. However, in order to compute with Grobner 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 is at most 50.
Eriksen Eivind
Gustavsen Trond S.
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