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Implementing the Kustin-Miller complex construction. (English) Zbl 1311.13012

Summary: The Kustin-Miller complex construction, due to A. Kustin and M. Miller, can be applied to a pair of resolutions of Gorenstein rings with certain properties to obtain a new Gorenstein ring and a resolution of it. It gives a tool to construct and analyze Gorenstein rings of high codimension. We describe the Kustin-Miller complex, its implementation in the Macaulay2 package KustinMiller, and explain how it can be applied to explicit examples.

MSC:

13D02 Syzygies, resolutions, complexes and commutative rings
13P20 Computational homological algebra
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13F55 Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes
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