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.


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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